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RESEARCH PRODUCT
Abelian Sylow subgroups in a finite group, II
Gabriel NavarroRonald SolomonPham Huu Tiepsubject
p-groupCombinatoricsMathematics::Group TheoryNormal p-complementAlgebra and Number TheoryLocally finite groupSylow theoremsCyclic groupElementary abelian groupOmega and agemo subgroupAbelian groupMathematicsdescription
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 ).
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-01-01 | Journal of Algebra |