0000000000425083

AUTHOR

Ronald Solomon

showing 2 related works from this author

Nilpotent and abelian Hall subgroups in finite groups

2015

[EN] We give a characterization of the finite groups having nilpotent or abelian Hall pi-subgroups that can easily be verified using the character table.

AlgebraNilpotentPure mathematicsApplied MathematicsGeneral MathematicsSylow theoremsabelian Hall subgroupsAbelian groupSYLOWMATEMATICA APLICADAnilpotent all subgroupsfinite groupsMathematics
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Abelian Sylow subgroups in a finite group, II

2015

Abstract Let p ≠ 3 , 5 be a prime. We prove that Sylow p-subgroups of a finite group G are abelian if and only if the class sizes of the p-elements of G are all coprime to p. This gives a solution to a problem posed by R. Brauer in 1956 (for p ≠ 3 , 5 ).

p-groupCombinatoricsMathematics::Group TheoryNormal p-complementAlgebra and Number TheoryLocally finite groupSylow theoremsCyclic groupElementary abelian groupOmega and agemo subgroupAbelian groupMathematicsJournal of Algebra
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