Action of a Frobenius-like group with kernel having central derived subgroup


Creative Commons License

Ercan G. , Güloğlu İ. Ş.

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, vol.26, pp.1257-1265, 2016 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 26
  • Publication Date: 2016
  • Doi Number: 10.1142/s0218196716500533
  • Title of Journal : INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
  • Page Numbers: pp.1257-1265

Abstract

A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that [F, h] = F for all nonidentity elements h is an element of H. Suppose that a finite group G admits a Frobenius-like group of auto-morphisms FH of coprime order with [F', H] = 1. In case where C-G( F) = 1 we prove that the groups G and C-G( H) have the same nilpotent length under certain additional assumptions.