Groups of automorphisms with TNI-centralizers

Ercan G., Güloğlu İ. Ş.

JOURNAL OF ALGEBRA, vol.498, pp.38-46, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 498
  • Publication Date: 2018
  • Doi Number: 10.1016/j.jalgebra.2017.10.021
  • Journal Name: JOURNAL OF ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.38-46
  • Middle East Technical University Affiliated: Yes

Abstract

A subgroup H of a finite group G is called a TNI-subgroup if N-G(H) boolean AND H-9 = 1 for any g is an element of G \ N-G (H). Let A be a group acting on G by automorphisms where C-G(A) is a TNI-subgroup of G. We prove that G is solvable if and only if C-G(A) is solvable, and determine some bounds for the nilpotent length of G in terms of the nilpotent length of C-G(A) under some additional assumptions. We also study the action of a Frobenius group FH of automorphisms on a group G if the set of fixed points C-G(F) of the kernel F forms a TNI-subgroup, and obtain a bound for the nilpotent length of G in terms of the nilpotent lengths of C-G(F) and C-G(H). (C) 2017 Elsevier Inc. All rights reserved.