FIXED-POINT FREE ACTION OF AN ABELIAN GROUP OF ODD NON-SQUAREFREE EXPONENT


ERCAN G., GÜLOĞLU İ. Ş. , Sagdicoglu O. M.

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, vol.54, pp.77-89, 2011 (SCI-Expanded) identifier identifier

Abstract

Let A be a finite group acting fixed-point freely on a finite (solvable) group G. A longstanding conjecture is that if (vertical bar G vertical bar, vertical bar A vertical bar) = 1, then the Fitting length of G is bounded by the length of the longest chain of subgroups of A. It is expected that the conjecture is true when the coprimeness condition is replaced by the assumption that A is nilpotent. We establish the conjecture without the coprimeness condition in the case where A is an abelian group whose order is a product of three odd primes and where the Sylow 2-subgroups of G are abelian.