0000000000425083
AUTHOR
Ronald Solomon
Nilpotent and abelian Hall subgroups in finite groups
[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.
Abelian Sylow subgroups in a finite group, II
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 ).