Abelian Sylow subgroups in a finite group, II

作者：Navarro Gabriel; Solomon Ronald^*; Pham Huu Tiep

来源：Journal of Algebra, 2015, 421: 3-11.

DOI：10.1016/j.jalgebra.2014.08.012

• Abelian Sylow subgroups

Let p 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, and, if p is an element of{3, 5}, the degree of every irreducible character in the principal p-block of G is coprime to p. This gives a complete solution to a problem posed by R. Brauer in 1963.

• 出版日期2015-1-1