Extensions of several coprime results to good action case

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Ercan G., Guloglu I. S., Jabara E.

Journal of Algebra and its Applications, vol.21, no.11, 2022 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 11
  • Publication Date: 2022
  • Doi Number: 10.1142/s021949882250222x
  • Journal Name: Journal of Algebra and its Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Good action, fitting height, fixed point free action, supersolvable, p-nilpotent
  • Open Archive Collection: AVESIS Open Access Collection
  • Middle East Technical University Affiliated: Yes

Abstract

Let G and A be groups where A acts on G by automorphisms. We say "the action of A on G is good"if the equality H = [H,B]CH(B) holds for any subgroup B of A and for any B-invariant subgroup H of G. It is straightforward that every coprime action is a good action. In this work, we extend some results due to Ward, Gross, Shumyatsky, Jabara and Meng and Guo under coprime action to good action.