Finite groups admitting a dihedral group of automorphisms


Ercan G. , Güloğlu İ. Ş.

ALGEBRA & DISCRETE MATHEMATICS, vol.23, pp.223-229, 2017 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 23
  • Publication Date: 2017
  • Title of Journal : ALGEBRA & DISCRETE MATHEMATICS
  • Page Numbers: pp.223-229

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).