wiktionary Socle may refer to Socle mathematics Socle architecture disambig Long comment to avoid being listed on short pages pl Cok ujednoznacznienie ... more details
In mathematics , the term socle has several related meanings. Socle of a group In the context of group theory , the socle of a group mathematics group G , denoted soc G , is the subgroup generated by the minimal normal subgroup s of G . It can happen that a group has no minimal non trivial normal subgroup that is, every non trivial normal subgroup properly contains another such subgroup and in that case the socle is defined to be the subgroup generated by the identity. The socle is a direct product of minimal normal subgroups sfn Robinson 1996 loc p.87 . As an example, consider the cyclic group Z sub 12 sub with generating set of a group generator u , which has two minimal normal subgroups, one generated by u sup 4 sup which gives a normal subgroup with 3 elements and the other by u sup 6 sup which gives a normal subgroup with 2 elements . Thus the socle of Z sub 12 sub is the group generated by u sup 4 sup and u sup 6 sup , which is just the group generated by u sup 2 sup . The socle is a characteristic subgroup , and hence a normal subgroup. It is not necessarily Transitively normal subgroup transitively normal , however. If a group G is a finite solvable group , then the socle is can be expressed as a product of elementary abelian p group p groups . Thus, in this case, it just a product of copies of Z pZ for various p where the same p may occur multiple times in the product. Socle of a module In the context of module theory and ring theory the socle of a module mathematics ..., math mathrm soc M bigcap E mid E mbox is an essential submodule of M , math The socle of a ring R can ... modules is semisimple, the socle of a module could also be defined as the unique maximal ... R module then the socle consists precisely of the elements annihilated by the Jacobson radical of R ... Socle of a Lie algebra In the context of Lie algebra s, a socle of a symmetric Lie algebra is the eigenspace ... decomposes into the direct sum of modules direct sum of its socle and cosocle . ref Mikhail Postnikov ... more details
In architecture , a socle is a short plinth used to support a pedestal , sculpture or column. In the field of archaeology, this term is used to refer to a wall base, frequently of stone, that supports the upper part of the wall, which is made of a different material, frequently mud brick. Citation needed date February 2008 This was a typical building practice for ancient Greece, resulting in the frequent preservation of the plans of ancient buildings only in their stone built lower walls, as at the city of Olynthos . Citation needed date February 2008 References Merriam Webster Online Dictionary Architecturalelement stub Category Architectural elements io Soklo it Zoccolo architettura pl Cok fi Sokkeli sv Sockel ... more details
In mathematics , the term cosocle has several related meanings. In group theory , a cosocle of a group mathematics group G , denoted by Cosoc G , is the intersection of all maximal subgroup maximal normal subgroup s of G . ref name abb Adolfo Ballester Bolinches, Luis M. Ezquerro, Classes of Finite Groups , 2006, ISBN 1402047185, http books.google.com books?id VoQ53SosWLIC&pg PA97&dq cosocle v onepage&q cosocle&f false p. 97 ref If G is a quasisimple group , then Cosoc G Center group theory Z G . ref name abb In the context of Lie algebra s, a cosocle of a symmetric Lie algebra is the eigenspace of its structural automorphism which corresponds to the eigenvalue 1. A symmetric Lie algebra decomposes into the direct sum of modules direct sum of its socle mathematics socle and cosocle. ref Mikhail Postnikov , Geometry VI Riemannian Geometry , 2001, ISBN 3540411089, http books.google.com books?id P60o2UKOaPcC&pg PA98&dq cosocle v onepage&q socle&f false p. 98 ref See also Socle mathematics Socle References reflist Category Group theory Abstract algebra stub ... more details
In mathematics , in the theory of Module mathematics module s, the radical of a module is a component in the theory of structure and classification. It is a generalization of the Jacobson radical for ring theory ring s. In many ways, it is the duality mathematics dual notion to that of the socle mathematics socle soc M of M . Definition Let R be a Ring mathematics ring and M a left R module. A submodule N of M is called maximal submodule maximal or cosimple if the quotient M N is a simple module . The radical of the module M is the intersection of all maximal submodules of M , math mathrm rad M bigcap N mid N mbox is a maximal submodule of M , math Equivalently, math mathrm rad M sum S mid S mbox is a superfluous submodule of M , math These definitions have direct dual analogues for soc M . Properties In addition to the fact rad M is the sum of superfluous submodules, in a Noetherian module rad M itself is a superfluous submodule . A ring for which rad M 0 for every right R module M is called a right V ring . For any module M , rad M rad M is zero. M is a finitely generated module if and only if M rad M is finitely generated and rad M is a superfluous submodule of M . See also Socle mathematics Jacobson radical References cite book last Alperin first J.L. author link J. L. Alperin coauthors Rowen B. Bell title Groups and representations publisher Springer Verlag year 1995 isbn 0 387 94526 1 pages 136 cite book last Anderson first Frank Wylie coauthors Kent R. Fuller title Rings and Categories of Modules publisher Springer Verlag isbn 978 0 387 97845 1 year 1992 Category Module theory Abstract algebra stub ... more details
In mathematical finite group theory, a rank 3 permutation group is a group acting transitively on a set such that the stabilizer of a point has 3 orbits. The study of these groups was started by harvs txt authorlink Donald Higman last Higman year1 1964 year2 1971 . Several of the sporadic simple group s were discovered as rank 3 permutation groups. Classification The primitive rank 3 permutation groups are all in one of the following classes harvtxt Cameron 1981 classified the ones such that math T times T le G le T 0 rm wr Z 2Z math where the Socle mathematics socle T of T sub 0 sub is simple, and T sub 0 sub is a 2 transitive group of degree n . harvtxt Liebeck 1987 classified the ones with a regular elementary abelian normal subgroup harvtxt Bannai 1971 classified the ones whose socle is a simple alternating group harvtxt Kantor Liebler 1982 classified the ones whose socle is a simple classical group harvtxt Liebeck Saxl 1986 classified the ones whose socle is a simple exceptional or sporadic group References Citation last1 Bannai first1 Eiichi title Maximal subgroups of low rank of finite symmetric and alternating groups mr 0357559 year 72 month 1971 journal Journal of the Faculty of Science. University of Tokyo. Section IA. Mathematics issn 0040 8980 volume 18 pages 475 486 Citation last1 Brouwer first1 A. E. last2 Cohen first2 A. M. last3 Neumaier first3 Arnold title Distance regular graphs publisher Springer Verlag location Berlin, New York series Ergebnisse der Mathematik und ihrer Grenzgebiete 3 Results in Mathematics and Related Areas 3 isbn 978 3 540 50619 5 mr 1002568 year 1989 volume 18 Citation last1 Cameron first1 Peter J. title Finite permutation groups and finite simple groups doi 10.1112 blms 13.1.1 mr 599634 year 1981 journal The Bulletin of the London Mathematical Society issn 0024 6093 volume 13 issue 1 pages 1 22 Citation last1 Higman first1 Donald G. author1 link Donald G. Higman title Finite permutation groups of rank 3 doi 10.1007 BF01111335 ... more details
In mathematics, a Loewy ring or semi Artinian ring is a ring in which every non zero module mathematics module has a non zero socle mathematics socle , or equivalently if the Loewy length of every module is defined. The concepts are named after Alfred Loewy . Loewy length The Loewy length and Loewy series were introduced by harvs txt last1 Artin first1 Emil author1 link Emil Artin last2 Nesbitt first2 Cecil J. last3 Thrall first3 Robert M. title Rings with Minimum Condition url http books.google.com books?id ZOcyYgEACAAJ publisher University of Michigan Press location Ann Arbor series University of Michigan Publications in Mathematics, no. 1 mr 0010543 year 1944 If M is a module, then define the Loewy series M sub sub for ordinal number ordinals by M sub 0 sub 0, M sub 1 sub M sub sub socle M M sub sub , M sub sub sub sub M sub sub if is a limit ordinal. The Loewy length of M is defined to be the smallest with M M sub sub , if it exists. References Citation last1 Artin first1 Emil author1 link Emil Artin last2 Nesbitt first2 Cecil J. last3 Thrall first3 Robert M. title Rings with Minimum Condition url http books.google.com books?id ZOcyYgEACAAJ publisher University of Michigan Press location Ann Arbor series University of Michigan Publications in Mathematics, no. 1 mr 0010543 year 1944 Citation last1 Nastasescu first1 Constantin last2 Popescu first2 Nicolae title Anneaux semi artiniens url http www.numdam.org item?id BSMF 1968 96 357 0 mr 0238887 year 1968 journal Bulletin de la Soci t Math matique de France issn 0037 9484 volume 96 pages 357 368 Category Ring theory ... more details
File Scultrinasc.jpg thumb 250px Tomb of Cardinal Brancacci. File Assunzione della verginje, donatello.jpg thumb 250px Donatello s relief of the Assumption of the Virgin . The Tomb of Cardinal Rainaldo Brancacci or Brancaccio is a sculptural work in the church of Sant Angelo a Nilo in Naples , southern Italy, executed by Donatello and Michelozzo around 1426 1428. Built in marble, partly gilt and polychrome, it has a height of 11.60 meters and a width of 4.60. History The work was produced during the partnership of Donatello and Michelozzo, which lasted from 1425 until the late 1430s. It was commissioned when Brancacci was still alive a letter to him of 5 June 1427 mentions the work as completed for some one quarter. In 1426 the two rented a workshop in Pisa , from where the pieces of the tomb could be more easily shipped to Naples by sea the city was also nearer to the marble quarries of Carrara . Assistants, including perhaps Pagno di Lapo Portigiani , collaborated to the work, which was completed and sent to its destination in 1428. Description The work is based on a socle architecture socle from which two composite columns start. They support a round arch with side pendentive s decorated by chamfered pilasters and tondo reliefs. At the top is the cusp, in Gothic sculpture Gothic style with, at the centre, a relief tondo of Christ Redeemer and two statues of puttos with trumpets an allusion to the biblical Apocalypse and the resurrection of the dead . The tomb itself is enclosed in the architectural frame, supported by three caryatid s. The sarcophagus front has two coat of arms at the sides, and a stiacciato relief of the Assumption of the Virgin executed by Donatello. Above it is the lying portrait of the cardinal and two angels who are opening a stone drapery hanging from the arch. Behind them is a lunette with a bas relief of the Madonna between Two Saints . See also Tomb of Antipope John XXIII Sources cite book first Rolf C. last Wirtz title Donatello publish ... more details
In the context of a module mathematics module M over a ring mathematics ring R , the top of M is the largest semisimple module semisimple quotient module of M if it exists. For finite dimensional k algebras k a field , if rad M denotes the intersection of all proper maximal submodule s of M the radical of a module radical of the module , then the top of M is M rad M . In the case of local rings with maximal ideal P , the top of M is M PM . In general if R is a semilocal ring semi artinian ring , that is, if R Rad R is an Artinian ring , where Rad R is the Jacobson radical of R , then M rad M is a semisimple module and is the top of M . This includes the cases of local rings and finite dimensional algebras over fields. See also Projective cover Radical of a module Socle mathematics References David Eisenbud , Commutative algebra with a view toward Algebraic Geometry ISBN 0 387 94269 6 Category Commutative algebra Category Module theory Abstract algebra stub ... more details
Ak Astana Baba is a mausoleum that is located in the Surxondaryo Province of Uzbekistan The mausoleum is being considered for inscription as a UNESCO World Heritage site. Site Description blockquote The mausoleum has centric composition, square in plan and oriented to all World s parts. The cubiform construction is flanked by guldusta towers and crowned by well proportioned sphere conical dome. Octahedron with arches is decorating dome s ceiling. North east, north west and south west walls of the interior have rather deep lancet bays with two twelve sided columns. The room with grave stone sagana is lightened by hole in sophit of the entrance arch. Fa ades are decorated by figured brickwork with wide vertical seams. Upper row of brickwork is sloped. Socle, the first ring and two rows of brickwork made from large bricks. blockquote ref http whc.unesco.org en tentativelists 810 ref World Heritage Status This site was added to the UNESCO World Heritage Tentative List on June 1, 1996, in the Cultural category. References reflist coord missing Uzbekistan Category World Heritage Sites in Uzbekistan ... more details
Infobox Award name Lennart Johanssons Pokal image Lennart Johanssons Pokal.JPG imagesize 200px year 2001 holder Helsingborgs IF description Winning Allsvenskan presenter Swedish Football Association website http www.svenskfotboll.se svenskfotboll.se Lennart Johanssons Pokal is a trophy awarded annually by the Swedish Football Association to the Association football football club that wins Allsvenskan , Swedens highest football league. The trophy was introduced in 2001 after it had become known that Clarence von Rosen , the man after which the previous trophy was named, had Nazi Party nazi sympathies during the 1930 s. ref name SM pokalen ska skrotas Cite web last Thor n first Petra url http wwwc.aftonbladet.se sport 0012 13 pokal.html title SM pokalen ska skrotas work aftonbladet.se accessdate 2011 01 03 language Swedish ref The first club to lift the trophy was Hammarby IF in 2001 Allsvenskan 2001 and most recently Helsingborgs IF in 2011 Allsvenskan 2011 . Djurg rdens IF Fotboll Djurg rdens IF are the club to lift the trophy the most times having lifted it in 2002 Allsvenskan 2002 , 2003 Allsvenskan 2003 and 2005 Allsvenskan 2005 . The trophy The trophy is made of silver and has a Football soccer football mounted on a Socle architecture socle with two large handles on each side of the socle. The trophy was designed by Anja Nibbler Kothe and was inspired by a trophy that the Sweden national football team had been awarded for winning the gold medal at the Football at the 1948 Summer Olympics 1948 Summer Olympics in London , United Kingdom . The trophy is named after Lennart Johansson , chairman of UEFA between 1990 and 2007. The thought behind the trophy was to connect the biggest trophy a Swedish club could win with the biggest Swedish football leader. Secret inscription controversy In 2010 Dagens Nyheter wrote an article where goldsmith Peter Gustafsson told the newspaper that his old colleague Ingemar Eklund who made the trophy had engraved Bajen Forever on the i ... more details
File Roma014a.jpg 450px right thumb Ponte Vittorio Emanuele II Ponte Vittorio Emanuele II is a bridge in Rome constructed to designs of 1886 by the architect Ennio De Rossi . Construction was delayed, and it was not inaugurated until 1911. The bridge across the Tiber connects the historic centre of Rome Corso Vittorio Emanuele, whose axis the bridge extends, and piazza Paoli at the bridgehead with the Borgo rione of Rome rione Borgo and the Vatican City , close to the few remains of the Roman Pons Neronianus . ref Remains of the Roman pier footings, just projecting above water level, can be seen through the leftmost arch in the illustration. ref The bridge commemorating Vittorio Emanuele II of Italy is carried in three arches spanning a distance of 108 metres. It is decorated at the ends with high socle architecture socles carrying colossal bronze winged Victories and over each of the Pier architecture piers with massive allegorical travertine sculptural groups. ref Touring Club Italiano, Roma e dintorni , 1965 241. ref Commons category Ponte Vittorio Emanuele II Notes Reflist coord 41 54 04 N 12 27 51 E type landmark source kolossus itwiki display title DEFAULTSORT Vittorio Emanuele Ii Category Bridges in Rome Category Bridges completed in 1911 Italy bridge struct stub it Ponte Vittorio Emanuele II ... more details
Infobox station name Pecherska type METROKIEV type style Syretsko Pecherska image Pecherska metro station Kiev 2010 01.jpg image size image caption address coordinates coord 50 25 39 N 30 32 20 E region UA type landmark scale 5000 display title,inline line KIEVMETRO line3 other structure underground platform 1 depth levels 1 tracks 2 parking bicycle baggage check opened 1997 12 30 closed rebuilt electrified Yes ADA code 317 owned Kiev Metro zone smartcardname smartcardstatus former passengers pass year pass percent pass system mpassengers services s rail title Kiev Metro s line system METROKIEV line Syretsko Pecherska previous Klovska next Druzhby Narodiv map locator Pecherska lang ua is a station on Kiev Metro s Syretsko Pecherska Line . Originally planned to open along with the main section of the line which in late 1991, problems with the escalator tunnel meant that work was delayed, and the station finally opened only six years later on December 27, 1997. Designed by architects V.Gnevyshev, M.Alyoshkin and T.Tselokovskaya, Pecherska is a composition that was finalised still under Soviet influence, but slightly re modeled prior to its opening in mid 1990s. The traditional pylon trivault retains the common white marbled pylons, but adds newly introduced features such as a suspended ceiling that conceals the lighting instruments. Both the suspended vault and the open regions a pattern which repeats the steps of the pylons are faced with white and brown aluminium boards respectively. On the platform halls, the brown boards extend right up to the upper socle regions which are replaced with white ones that continue the curvature right up to the socle region above the tracks in place of a traditional marble wall . Lighting is provided by Sodium lamps hidden in the ends of the ceiling and by an additional long cross shaped elements that run the length of the vault in the central hall. Whilst the floor retains the grey granite. Pecherska is named after the Pech ... more details
tiara and veil, the veil wound under her chin, wearing a tunic and cloak, inscribed on the socle VESTA, on turned marble socle, early 19th Century publisher Christies.com date 1992 07 07 accessdate ... more details
by two upper or lower triangular matrix ring is not right or left Kasch. A ring with right Socle mathematics Socle of a module socle zero i.e. math mathrm soc R R 0 math cannot be right Kasch, since the ring ... more details
Image Plinth.jpg thumb 200px An ancient Greek plinth. In architecture , a plinth is the base or platform upon which a column , pedestal , statue , monument or structure rests. ref cite book first John C. last Poppeliers authorlink coauthors year 1983 title What Style is it? edition publisher John Wiley & Sons location New York pages 104 isbn 0 471 14434 7 ref Gottfried Semper s The Four Elements of Architecture 1851 posited that the plinth, the hearth , the roof, and the wall make up all of architectural theory. The plinth usually rests directly on the ground, or stylobate . According to Semper, the plinth exists to negotiate between a structure and the ground. Semper s theory has been influential in the development of architecture. ref Mallgrave, Harry Francis. Modern Architectural Theory A Historical Survey, 1673 1968 Cambridge, 2005 . ISBN 0 521 79306 8 ref Many houses in flood prone rural areas of Bangladesh are built on plinths homestead plinths . The word is also used for the base of a cabinet furniture cabinet or an audio phonograph turntable . Citation needed date October 2010 In dam engineering, the plinth is the link between the ground and the dam. For the case of arch dams, the term is changed to pulvino . See also wiktionary plinth Club foot furniture Set off architecture Dado architecture Socle architecture References reflist Category Architectural elements element arch stub bs Plinta de Plinthe es Plinto eo Plinto gl Plinto hi io Plinto it Plinto nl Sokkel beeld pl Plinta pt Plinto ro Plint sa sr sh Plinta ... more details
Platform for Change, Unity and Democracy , abbreviated as S.C.U.D. Socle pour le Changement, l Unit et la D mocratie in French language French , is a Chad ian Rebellion rebel group that was formed in October 2005 by former members of the Military of Chad who deserted and united under founders and current leaders, 30 year old Yaya Dillo Dj rou and his brother. The group s main objective is to oust the government of the current Chadian president, and uncle of Dj rou and his brother, Idriss D by . http www.strategypage.com qnd chad articles 20051220.aspx SCUD has bases in eastern Chad and in the Darfur region of Sudan . On December 18, 2005, SCUD, along with members of the Rally for Democracy and Liberty RDL rebel group, Second Battle of Adr attacked Chadian troops stationed in the city of Adr , sparking the Chadian Sudanese conflict . Massimo Giovanola of Cooperazione Internazionale said, D by is said to have got to the point of offering the rebels 400 million CFA francs about 600,000 to put down their arms... but it s not a question of money. D by has acquired too much power in recent years and the Zaghawa people Zaghawa have decided to get rid of him. External links http www.strategypage.com qnd chad articles 20051220.aspx War Breaks Out on Sudan Border &mdash Strategy Page accessed December 29, 2005 Chadian Sudanese conflict Category Second Chadian Civil War Category Politics of Chad Category Rebel groups in Chad Chad stub Africa mil stub de Plattform f r Wandel, Einheit und Demokratie ... more details
Scud is the popularized term for a series of tactical ballistic missiles developed by the Soviet Union during the Cold War. Scud may also refer to Scud animal a shrimplike aquatic crustacean Septicemic cutaneous ulcerative disease SCUD a disease found in turtles Scud cloud low, detached clouds Scud running an aviation term Scud Nautical Term For a ship to run before a strong wind, carrying little or no sail. Scud Sailplane a 1930s glider produced by Abbott Baynes Sailplanes Ltd Irn Bru , the Scottish soft drink, is referred to as Scud in some Scottish slang Scud Mountain Boys American country music band Scud Race Sega Super GT in North America an arcade racing game by Sega Scud The Disposable Assassin science fiction comic book Scud The Disposable Assassin video game Scud The Disposable Assassin A video game for the Sega Saturn Radio 4 News FM Scud FM BBC Radio 4 continuous Gulf War news service Special Counter terrorist Unit Delta the original name of G.I. Joe Team G.I. Joe Socle pour le changement, l unit et la d mocratie People named Scud Scud film producer writer the stage name of director Danny Cheng Wan Cheung Arthur Kent Canadian journalist for NBC nicknamed The Scud Stud Rageh Omaar Somali born journalist for the BBC nicknamed The Scud Stud DJ Scud English DJ Mark Philippoussis Australian tennis player nicknamed Scud Scud in Blade II played by Norman Reedus List of Toy Story characters Scud is Sid s dog in Toy Story disambig ... more details
stories of the building are faced with big uncut blocks of a Tulchyn labradorite , while Socle architecture socle and Portal architecture portal s with a polished granite . Alloy metal flagpoles and decorated ... more details
In mathematics , especially in areas of abstract algebra and finite geometry , the list of transitive finite linear groups is an important classification of certain highly symmetric group action actions of finite group s on vector space s. The solvable group solvable finite 2 transitive group s were classified by Bertram Huppert . ref Citation last1 Huppert first1 Bertram author1 link Bertram Huppert title Zweifach transitive, aufl sbare Permutationsgruppen doi 10.1007 BF01160336 id MathSciNet id 0094386 year 1957 journal Mathematische Zeitschrift issn 0025 5874 volume 68 pages 126 150 ref The classification of finite simple groups made possible the complete classification of finite doubly transitive permutation groups . This is a result by Christoph Hering . ref Citation last1 Hering first1 Christoph title Transitive linear groups and linear groups which contain irreducible subgroups of prime order. II doi 10.1016 0021 8693 85 90179 6 id MathSciNet id 780488 year 1985 journal Journal of Algebra issn 0021 8693 volume 93 issue 1 pages 151 164 ref A finite 2 transitive group has a socle mathematics socle that is either a vector space over a finite field or a non abelian primitive simple group groups of the latter kind are almost simple groups and described elsewhere haha, where? someday at almost simple group ? . This article provides a complete and irredundant? list of the finite 2 transitive groups whose socle is elementary abelian group elementary abelian . Let math p math be a prime, and math G math a subgroup of the general linear group math GL d,p math acting transitively on the nonzero vectors of the d dimensional vector space math F p d math over the finite field math F p math with p elements. Infinite classes There are four infinite classes of finite transitive linear groups. math G leq Gamma L 1,p d math math G triangleright SL a,q text and p d q a math math G triangleright Sp 2a,q text and p d q 2a math math G triangleright G 2 q , p d q 6 text and p 2. mat ... more details
with the isomorphism types of simple modules the Socle mathematics socle of each projective indecomposable ... as a summand of the group algebra viewed as the regular module is the dimension of its socle for large ... Brauer character can thus be defined this is 0 if the second Brauer character is that of the socle of a non ... socle. The multiplicity of an ordinary irreducible character in the character of the lift of a projective indecomposable is equal to the number of occurrences of the Brauer character of the socle of the projective ... more details
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