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, 2021 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Publication Date: 2021
  • Doi Number: 10.1142/s021949882250222x
  • Journal Name: Journal of Algebra and its Applications
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Fitting height, Fixed point free action, Good action, P-nilpotent, Supersolvable

Abstract

© 2022 World Scientific Publishing Company.Let G and A be groups where A acts on G by automorphisms. We say "the action ofA onG 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.