Groups of automorphisms with TNI-centralizers

Ercan G., Güloğlu İ. Ş.

JOURNAL OF ALGEBRA, cilt.498, ss.38-46, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 498
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1016/j.jalgebra.2017.10.021
  • Dergi Adı: JOURNAL OF ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.38-46
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.