Finite groups admitting a dihedral group of automorphisms
ALGEBRA & DISCRETE MATHEMATICS, vol.23, pp.223-229, 2017 (Peer-Reviewed Journal)
- Publication Type: Article / Article
- Volume: 23
- Publication Date: 2017
- Journal Name: ALGEBRA & DISCRETE MATHEMATICS
- Page Numbers: pp.223-229
- Middle East Technical University Affiliated: Yes
Abstract
Let D = alpha, beta be a dihedral group generated by the involutions alpha and beta and let F = alpha beta). Suppose that D acts on a finite group G by automorphisms in such a way that C-G(F)= 1. In the present paper we prove that the nilpotent, length of the group Cr' is equal to the maximum of the nilpotent lengths of the subgroups C-G (alpha) and C-G(beta).