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, cilt.54, ss.77-89, 2011 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 54
  • Basım Tarihi: 2011
  • Doi Numarası: 10.1017/s0013091509000583
  • Dergi Adı: PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY
  • Sayfa Sayıları: ss.77-89

Özet

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.