On a Fitting length conjecture without the coprimeness condition

Ercan G.

MONATSHEFTE FUR MATHEMATIK, vol.167, pp.175-187, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 167
  • Publication Date: 2012
  • Doi Number: 10.1007/s00605-011-0287-3
  • Journal Name: MONATSHEFTE FUR MATHEMATIK
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.175-187
  • Keywords: Automorphisms of solvable groups, Noncoprime action, Fixedpoint free action, POINT FREE AUTOMORPHISMS, FINITE-GROUPS, SOLVABLE GROUPS
  • Middle East Technical University Affiliated: Yes

Abstract

Let A be a finite nilpotent group acting fixed point freely by automorphisms on the finite solvable group G. It is conjectured that the Fitting length of G is bounded by the number of primes dividing the order of A, counted with multiplicities. The main result of this paper shows that the conjecture is true in the case where A is cyclic of order p (n) q, for prime numbers p and q coprime to 6 and G has abelian Sylow 2-subgroups.