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In finite group theory, an area of abstract algebra, a strongly embedded subgroup of a finite group G is a proper subgroup H of even order such that H ∩ Hg has odd order whenever g is not in H. The Bender–Suzuki theorem, proved by extending work of Suzuki , classifies the groups G with a strongly embedded subgroup H. It states that either , part II) revised Suzuki's part of the proof. extended Bender's classification to groups with a proper 2-generated core.

Attributes	Values
rdf:type	yago:Abstraction100002137 yago:Group100031264 chemical compound yago:WikicatFiniteGroups
rdfs:label	Strongly embedded subgroup (en)
rdfs:comment	In finite group theory, an area of abstract algebra, a strongly embedded subgroup of a finite group G is a proper subgroup H of even order such that H ∩ Hg has odd order whenever g is not in H. The Bender–Suzuki theorem, proved by extending work of Suzuki , classifies the groups G with a strongly embedded subgroup H. It states that either , part II) revised Suzuki's part of the proof. extended Bender's classification to groups with a proper 2-generated core. (en)
dct:subject	Finite groups
Wikipage page ID	29523845 (xsd:integer)
Wikipage revision ID	1032104173 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Annals of Mathematics Normal subgroup Simple group Journal of Algebra Finite groups Quaternion group Involution (mathematics) Abstract algebra Finite group Transactions of the American Mathematical Society Proper subgroup Centralizer
Link from a Wikipage to an external page	https://books.google.com/books%3Fisbn=052164660X
sameAs	Strongly embedded subgroup Strongly embedded subgroup Strongly embedded subgroup Strongly embedded subgroup
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Harvtxt dbt:Harvs
has abstract	In finite group theory, an area of abstract algebra, a strongly embedded subgroup of a finite group G is a proper subgroup H of even order such that H ∩ Hg has odd order whenever g is not in H. The Bender–Suzuki theorem, proved by extending work of Suzuki , classifies the groups G with a strongly embedded subgroup H. It states that either 1. * G has cyclic or generalized quaternion Sylow 2-subgroups and H contains the centralizer of an involution 2. * or G/O(G) has a normal subgroup of odd index isomorphic to one of the simple groups PSL2(q), Sz(q) or PSU3(q) where q≥4 is a power of 2 and H is O(G)NG(S) for some Sylow 2-subgroup S. , part II) revised Suzuki's part of the proof. extended Bender's classification to groups with a proper 2-generated core. (en)
gold:hypernym	H
prov:wasDerivedFrom	wikipedia-en:Strongly_embedded_subgroup?oldid=1032104173&ns=0
page length (characters) of wiki page	2781 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Strongly_embedded_subgroup
is Link from a Wikipage to another Wikipage of	Classification of finite simple groups Bender's theorem Bender-Suzuki theorem Bender–Suzuki theorem 2-generated core
is Wikipage redirect of	Bender's theorem Bender-Suzuki theorem Bender–Suzuki theorem 2-generated core
is foaf:primaryTopic of	wikipedia-en:Strongly_embedded_subgroup

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