Action of a Frobenius-like group with fixed-point free kernel


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Ercan G. , Güloğlu İ. Ş.

JOURNAL OF GROUP THEORY, vol.17, pp.863-873, 2014 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 17
  • Publication Date: 2014
  • Doi Number: 10.1515/jgt-2014-0002
  • Title of Journal : JOURNAL OF GROUP THEORY
  • Page Numbers: pp.863-873

Abstract

We call a finite group Frobenius-like if it has a nontrivial nilpotent normal subgroup F possessing a nontrivial complement H such that [F,h] = F for all nonidentity elements h is an element of H. We prove that any irreducible nontrivial FH-module for a Frobenius-like group FH of odd order over an algebraically-closed field has an H-regular direct summand if either F is fixed-point free on V or F acts nontrivially on V and the characteristic of the field is coprime to the order of F. Some consequences of this result are also derived.