A GENERALIZED FIXED-POINT-FREE ACTION


Güloğlu İ. Ş. , Ercan G.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.12, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12
  • Publication Date: 2013
  • Doi Number: 10.1142/s0219498812501721
  • Title of Journal : JOURNAL OF ALGEBRA AND ITS APPLICATIONS

Abstract

In this paper we study the structure of a finite group G admitting a solvable group A of automorphisms of coprime order so that for any x epsilon C-G(A) of prime order or of order 4, every conjugate of x in G is also contained in C-G(A). Under this hypothesis it is proven that the subgroup [G, A] is solvable. Also an upper bound for the nilpotent height of [G, A] in terms of the number of primes dividing the order of A is obtained in the case where A is abelian.