Frobenius groups of automorphisms with almost fixed point free kernel

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Ercan G., Güloğlu İ. Ş.

JOURNAL OF ALGEBRA, vol.521, pp.384-389, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 521
  • Publication Date: 2019
  • Doi Number: 10.1016/j.jalgebra.2018.12.004
  • Journal Name: JOURNAL OF ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.384-389
  • Middle East Technical University Affiliated: Yes

Abstract

Let FH be a Frobenius group with kernel F and complement H, acting coprimely on the finite solvable group G by automorphisms. We prove that if C-G(H) is of Fitting length n then the index of the n-th Fitting subgroup F-n(G) in G is bounded in terms of vertical bar C-G(F)vertical bar and vertical bar F vertical bar. This generalizes a result of Khukhro and Makarenko [6] which handles the case n = 1. (C) 2018 Elsevier Inc. All rights reserved.