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In the area of modern algebra known as group theory, the Conway groups are the three sporadic simple groups Co1, Co2 and Co3 along with the related finite group Co0 introduced by (Conway , ). The largest of the Conway groups, Co0, is the group of automorphisms of the Leech lattice Λ with respect to addition and inner product. It has order 8,315,553,613,086,720,000 but it is not a simple group. The simple group Co1 of order 4,157,776,806,543,360,000 = 221 · 39 · 54 · 72 · 11 · 13 · 23 is defined as the quotient of Co0 by its center, which consists of the scalar matrices ±1. The groups Co2 of order

Attributes	Values
rdf:type	yago:WikicatSporadicGroups yago:Abstraction100002137 yago:Group100031264 movie
rdfs:label	Conway group (en) Groupes de Conway (fr) 콘웨이군 (수학) (ko) Conway-groep (nl) Группы Конвея (ru) 康威群 (zh)
rdfs:comment	군론에서 콘웨이 군(영어: Conway group)은 존 호턴 콘웨이가 도입한 산재군 , , 및 이와 관련된 유한군 Co0이다. 콘웨이 군 중 가장 큰 Co0는 덧셈 및 내적에 대한 리치 격자 Λ의 자기동형군으로, 위수 8,315,553,613,086,720,000을 갖고, 단순군이 아니다. 단순군 Co1은 Co0를 스칼라 행렬 ±1로 구성된 중심에 의한 몫군으로 정의되고, 위수 4,157,776,806,543,360,000를 갖는다. 리치 격자의 내적은 두 벡터의 스칼라곱의 1/8로 정의되고, 정수값을 갖는다. 벡터의 제곱 노름은 자신과의 내적이며 항상 짝수이다. 리치 격자의 벡터에 대해 그 제곱 노름의 절반을 벡터의 유형이라고 한다. 콘웨이 군의 부분군은 종종 관련된 고정점의 유형을 참조하여 이름이 붙는다. 리치 격자에는 유형 1의 벡터가 없다. (위수 42,305,421,312,000) 및 (위수 495,766,656,000)은 각각 유형 2와 유형 3의 격자 벡터를 고정하는 리치 격자 Λ의 자기동형으로 구성된다. 스칼라 −1은 영벡터가 아닌 벡터를 고정하지 않으므로 이 두 군은 Co1의 부분군과 동형이다. (ko) 康威群（英語：Conway group）Co1、Co2、Co3是三个散在群，由英国数学家约翰·何顿·康威发现。康威群都是通过利奇格（Leech lattice）构造得到的。它们的阶分别为： Co1：4,157,776,806,543,360,000 = 221 · 39 · 54 · 72 · 11 · 13 · 23Co2：42,305,421,312,000 = 218 · 36 · 53 · 7 · 11 · 23Co3：495,766,656,000 = 210 · 37 · 53 · 7 · 11 · 23 (zh) In the area of modern algebra known as group theory, the Conway groups are the three sporadic simple groups Co1, Co2 and Co3 along with the related finite group Co0 introduced by (Conway , ). The largest of the Conway groups, Co0, is the group of automorphisms of the Leech lattice Λ with respect to addition and inner product. It has order 8,315,553,613,086,720,000 but it is not a simple group. The simple group Co1 of order 4,157,776,806,543,360,000 = 221 · 39 · 54 · 72 · 11 · 13 · 23 is defined as the quotient of Co0 by its center, which consists of the scalar matrices ±1. The groups Co2 of order (en) En mathématiques, les groupes de Conway Co1, Co2 et Co3 sont trois groupes sporadiques découverts par John Horton Conway en 1968. Tous sont intimement liés au réseau de Leech Λ. Le plus grand, Co1, d'ordre 4 157 776 806 543 360 000, est obtenu en quotientant le groupe des automorphismes de Λ par son centre, qui est constitué des matrices scalaires ±1. (fr) In de groepentheorie, een deelgebied van de wiskunde, zijn de Conway-groepen , en , drie sporadische groepen die zijn ontdekt door John Horton Conway. Thomas Thompson beschrijft hoe John Leech rond 1964 dichte bolstapelingen in euclidische ruimten van hoge dimensie onderzocht. Een van Leech' ontdekkingen was een roosterpakking in de 24-dimensionale ruimte, gebaseerd op wat later het leech-rooster, , werd genoemd. Hij vroeg zich af of de symmetriegroep van dat rooster een interessante enkelvoudige groep bevatte, maar voelde dat hij hierbij hulp nodig had van iemand die beter vertrouwd was met de groepentheorie. Omdat veel wiskundigen aan wie hij dit vroeg, logischerwijs hun eigen agenda hadden, moest Leech nog tamelijk lang rondvragen, voordat hij John Conway kon overhalen het probleem te (nl) Группы Конвея — это три введённые Конвеем спорадические простые группы Co1, и вместе со связанной с ними конечной группой Co0. Наибольшая из групп Конвея, Co0, является группой автоморфизмов решётки Лича . Эта группа имеет порядок 8,315,553,613,086,720,000 Она не является простой группой. Простая группа Co1 порядка 4,157,776,806,543,360,000 определяется как факторгруппа группы Co0 по её центру, который состоит из скалярных матриц ±1. (ru)
dcterms:subject	John Horton Conway Sporadic groups
Wikipage page ID	345511 (xsd:integer)
Wikipage revision ID	1100191285 (xsd:integer)
Link from a Wikipage to another Wikipage	Quaternion Module (mathematics) Monster group Dedekind eta function Permutation matrices Matrix (mathematics) Generalized permutation matrix Orthogonal Symmetric matrix Monstrous moonshine Conjugacy class Conway group Co1 Conway group Co2 Conway group Co3 Proceedings of the National Academy of Sciences Leech lattice Hall–Janko graph Journal of Algebra Suzuki sporadic group Mathieu group M24 Transpose G2 (mathematics) John Horton Conway Oxford University Press Robert Griess Group action (mathematics) Involution (mathematics) Sporadic groups Academic Press John G. Thompson John Horton Conway John Leech (mathematician) Binary Golay code Higman–Sims group Holomorph (mathematics) Diagonal matrices Dot product Automorphism group Group theory Inner product Michio Suzuki (mathematician) Order (group theory) Mathematical Association of America McLaughlin group (mathematics) Fischer group Mathieu groups Hall–Janko group Springer-Verlag Center of a group Complex structure on a real vector space Sporadic simple group
Link from a Wikipage to an external page	https://books.google.com/books%3Fid=upYwZ6cQumoC http://brauer.maths.qmul.ac.uk/Atlas/v3/spor/Co1/ https://books.google.com/books%3Fid=38fEMl2-Fp8C https://books.google.com/books%3Fid=TPPkAAAAIAAJ https://books.google.com/books%3Fid=YRdCAAAAIAAJ https://books.google.com/books%3Fid=ggqxuG31B3cC https://web.archive.org/web/20051110090124/http:/web.mat.bham.ac.uk/atlas/v2.0/spor/Co1/
sameAs	Conway group Conway group Conway group Conway group Conway group Conway group Conway group Conway group Conway group
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Harv dbt:Harvtxt dbt:Val dbt:· dbt:OEIS2C dbt:Abs dbt:Harvs dbt:Group_theory_sidebar
authorlink	John Horton Conway (en)
last	Conway (en)
year	1968 (xsd:integer) 1969 (xsd:integer)

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