WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 14, 2015
The Influence of Conjugacy Class Sizes on the Structure of Finite Groups
Author:
Abstract: Let G be a finite p-solvable group and let G* be the set of p′-elements of primary and biprimary orders of G. We show that when the conjugacy class sizes of G* are {1, m,p^a,mp^a} with (m,p) = 1, then the p-complements of G are nilpotent and m is a prime power.