Good action on a finite group

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Ercan G., Güloğlu İ. Ş., Jabara E.

JOURNAL OF ALGEBRA, vol.560, pp.486-501, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 560
  • Publication Date: 2020
  • Doi Number: 10.1016/j.jalgebra.2020.05.032
  • Journal Name: JOURNAL OF ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.486-501
  • Keywords: Solvable group, Automorphism, Fitting height, Fixed point free action, Regular module, POINT FREE ACTION, FREE AUTOMORPHISMS, FITTING LENGTH
  • Middle East Technical University Affiliated: Yes

Abstract

Let G and A be finite groups with A acting on G by automorphisms. In this paper we introduce the concept of "good action"; namely we say the action of A on G is good, if H = [H, B]C-H (B) for every subgroup B of A and every B-invariant subgroup H of G. This definition allows us to prove a new noncoprime Hall-Higman type theorem.