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- Benders_method abstract "In group theory, Bender's method is a method introduced by Bender (1970) for simplifying the local group theoretic analysis of the odd order theorem. Shortly afterwards he used it to simplify the Walter theorem on groups with abelian Sylow 2-subgroups Bender (1970b), and Gorenstein and Walter's classification of groups with dihedral Sylow 2-subgroups. Bender's method involves studying a maximal subgroup M containing the centralizer of an involution, and its generalized Fitting subgroup F*(M).One succinct version of Bender's method is the result that if M, N are two distinct maximal subgroups of a simple group with F*(M) ≤ N and F*(N) ≤ M, then there is a prime p such that both F*(M) and F*(N) are p-groups. This situation occurs whenever M and N are distinct maximal parabolic subgroups of a simple group of Lie type, and in this case p is the characteristic, but this has only been used to help identify groups of low Lie rank. These ideas are described in textbook form in Gagen (1976, p. 43),Huppert & Blackburn (1982, Chapter X. 15), Gorenstein, Lyons & Solomon (1996, p. 110, Chapter F.19), and Kurzweil & Stellmacher (2004, Chapter 10.1).".
- Benders_method wikiPageExternalLink 1256053074.
- Benders_method wikiPageExternalLink surv402.
- Benders_method wikiPageID "28055690".
- Benders_method wikiPageLength "3468".
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- Benders_method wikiPageRevisionID "571156343".
- Benders_method wikiPageWikiLink American_Mathematical_Society.
- Benders_method wikiPageWikiLink Cambridge_University_Press.
- Benders_method wikiPageWikiLink Category:Group_theory.
- Benders_method wikiPageWikiLink Centralizer_and_normalizer.
- Benders_method wikiPageWikiLink Feit–Thompson_theorem.
- Benders_method wikiPageWikiLink Fitting_subgroup.
- Benders_method wikiPageWikiLink Group_theory.
- Benders_method wikiPageWikiLink Involution_(mathematics).
- Benders_method wikiPageWikiLink Mathematische_Zeitschrift.
- Benders_method wikiPageWikiLink Maximal_subgroup.
- Benders_method wikiPageWikiLink P-group.
- Benders_method wikiPageWikiLink Springer_Science+Business_Media.
- Benders_method wikiPageWikiLink Walter_theorem.
- Benders_method wikiPageWikiLinkText "Bender's method".
- Benders_method wikiPageUsesTemplate Template:Citation.
- Benders_method wikiPageUsesTemplate Template:Harvtxt.
- Benders_method subject Category:Group_theory.
- Benders_method hypernym Method.
- Benders_method type Software.
- Benders_method comment "In group theory, Bender's method is a method introduced by Bender (1970) for simplifying the local group theoretic analysis of the odd order theorem. Shortly afterwards he used it to simplify the Walter theorem on groups with abelian Sylow 2-subgroups Bender (1970b), and Gorenstein and Walter's classification of groups with dihedral Sylow 2-subgroups.".
- Benders_method label "Bender's method".
- Benders_method sameAs Q4887036.
- Benders_method sameAs m.0cmc04m.
- Benders_method sameAs Q4887036.
- Benders_method wasDerivedFrom Benders_method?oldid=571156343.
- Benders_method isPrimaryTopicOf Benders_method.