Fixed point free action on groups of odd order

Ercan G., GÜLOĞLU İ. Ş.

JOURNAL OF ALGEBRA, vol.320, no.1, pp.426-436, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 320 Issue: 1
  • Publication Date: 2008
  • Doi Number: 10.1016/j.jalgebra.2008.01.033
  • Journal Name: JOURNAL OF ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.426-436
  • Keywords: solvable groups, fixed point free action, finite groups, representations, FINITE-GROUPS
  • Middle East Technical University Affiliated: Yes

Abstract

Let A be a finite abelian group that acts fixed point freely on a finite (solvable) group G. Assume that vertical bar G vertical bar is odd and A is of squarefree exponent coprime to 6. We show that the Fitting length of G is bounded by the length of the longest chain of subgroups of A. (C) 2008 Elsevier Inc. All rights reserved.