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In mathematics, a Ree group is a group of Lie type over a finite field constructed by Ree from an exceptional automorphism of a Dynkin diagram that reverses the direction of the multiple bonds, generalizing the Suzuki groups found by Suzuki using a different method. They were the last of the infinite families of finite simple groups to be discovered. defined Ree groups over infinite fields of characteristics 2 and 3. and introduced Ree groups of infinite-dimensional Kac–Moody algebras.

Attributes	Values
rdf:type	yago:Abstraction100002137 yago:Group100031264 Band yago:WikicatFiniteGroups
rdfs:label	이임학 군 (ko) Ree group (en) Группа Ри (ru)
rdfs:comment	이임학 군 또는 리 군(영어: Ree group)은 이임학이 발견한 유한 단순군의 부류이다. 이임학이 발견한 2F4(22n+1)와 2G2(32n+1), 그리고 (Suzuki groups) 2B2의 세 종류가 있다. 모두 리 형 군(groups of Lie type)에 속한다. (ko) In mathematics, a Ree group is a group of Lie type over a finite field constructed by Ree from an exceptional automorphism of a Dynkin diagram that reverses the direction of the multiple bonds, generalizing the Suzuki groups found by Suzuki using a different method. They were the last of the infinite families of finite simple groups to be discovered. defined Ree groups over infinite fields of characteristics 2 and 3. and introduced Ree groups of infinite-dimensional Kac–Moody algebras. (en) Группы Ри — это группы лиева типа над конечным полем, которые построил Ри из исключительных автоморфизмов диаграмм Дынкина, которые обращают направление кратных рёбер, что обобщает , которые нашёл Судзуки, используя другой метод. Группы были последними открытыми в бесконечных семействах . Титс определил группы Ри над бесконечными полями характеристики 2 и 3. Титс и Хи ввели группы Ри бесконечномерных . (ru)
dcterms:subject	Finite groups
Wikipage page ID	1739637 (xsd:integer)
Wikipage revision ID	1051866154 (xsd:integer)
Link from a Wikipage to another Wikipage	American Journal of Mathematics Elimination theory List of finite simple groups Moufang octagon Annals of Mathematics Dynkin diagram Inventiones Mathematicae John Wiley & Sons Proceedings of the National Academy of Sciences Andrew Odlyzko Steiner system Journal of Algebra Steinberg group (Lie theory) Automorphism Janko group Janko group J1 Schur multiplier American Mathematical Society Finite groups Finite field Outer automorphism group Doubly transitive permutation representation Kac–Moody algebra Coxeter group Tits group Bulletin of the AMS Group of Lie type Société Mathématique de France Suzuki groups Pacific Journal of Mathematics BN pair Pseudo-reductive algebraic group Finite simple group Reductive algebraic group Walter's theorem
Link from a Wikipage to an external page	https://www.math.ucla.edu/~rst/ http://projecteuclid.org/euclid.pjm/1103039126 https://web.archive.org/web/20120910032654/http:/www.math.ucla.edu/~rst/ http://brauer.maths.qmul.ac.uk/Atlas/v3/exc/R27/ https://www.ams.org/journals/bull/1960-66-06/S0002-9904-1960-10523-X/home.html https://www.ams.org/journals/bull/1961-67-01/S0002-9904-1961-10527-2/home.html http://www.numdam.org/item%3Fid=SB_1960-1961__6__65_0 http://www.numdam.org/item%3Fid=SB_1988-1989__31__7_0 https://books.google.com/books%3Fid=54HO1wDNM_YC
sameAs	Ree group Ree group Ree group Ree group Ree group Ree group
dbp:wikiPageUsesTemplate	dbt:= dbt:Citation dbt:Harvtxt dbt:Main dbt:Math dbt:Mvar dbt:Overline dbt:Portal dbt:Harvs
authorlink	Rimhak Ree (en)
last	Thompson (en) Ree (en)
year	1960 (xsd:integer) 1961 (xsd:integer) 1967 (xsd:integer) 1972 (xsd:integer) 1977 (xsd:integer)
has abstract	In mathematics, a Ree group is a group of Lie type over a finite field constructed by Ree from an exceptional automorphism of a Dynkin diagram that reverses the direction of the multiple bonds, generalizing the Suzuki groups found by Suzuki using a different method. They were the last of the infinite families of finite simple groups to be discovered. Unlike the Steinberg groups, the Ree groups are not given by the points of a connected reductive algebraic group defined over a finite field; in other words, there is no "Ree algebraic group" related to the Ree groups in the same way that (say) unitary groups are related to Steinberg groups. However, there are some exotic pseudo-reductive algebraic groups over non-perfect fields whose construction is related to the construction of Ree groups, as they use the same exotic automorphisms of Dynkin diagrams that change root lengths. defined Ree groups over infinite fields of characteristics 2 and 3. and introduced Ree groups of infinite-dimensional Kac–Moody algebras. (en) 이임학 군 또는 리 군(영어: Ree group)은 이임학이 발견한 유한 단순군의 부류이다. 이임학이 발견한 2F4(22n+1)와 2G2(32n+1), 그리고 (Suzuki groups) 2B2의 세 종류가 있다. 모두 리 형 군(groups of Lie type)에 속한다. (ko) Группы Ри — это группы лиева типа над конечным полем, которые построил Ри из исключительных автоморфизмов диаграмм Дынкина, которые обращают направление кратных рёбер, что обобщает , которые нашёл Судзуки, используя другой метод. Группы были последними открытыми в бесконечных семействах . В отличие от групп Штейнберга, группы Ри не задаются точками редуктивной алгебраической группы, определённой над конечным полем. Другими словами, нет никакой «алгебраической группы Ри», связанной с группами Ри таким же образом, каким (скажем) унитарные группы связаны с группами Штейнберга. Однако существуют некоторые экзотические над несовершенными полями, построение которых связано с построением групп Ри, так как они используют те же экзотические автоморфизмы диаграммы Дынкина, которые меняют длины корней. Титс определил группы Ри над бесконечными полями характеристики 2 и 3. Титс и Хи ввели группы Ри бесконечномерных . (ru)
gold:hypernym	Group
prov:wasDerivedFrom	wikipedia-en:Ree_group?oldid=1051866154&ns=0
page length (characters) of wiki page	17084 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Ree_group
is Link from a Wikipage to another Wikipage of	List of finite simple groups Pseudo-reductive group Rimhak Ree Unital (geometry) Stephen Arthur Jennings Generalized polygon Enrico Bombieri Ree groups G2 (mathematics) Janko group J1 List of Korean Canadians List of Korean inventions and discoveries Hurwitz's automorphisms theorem

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