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Extensions of several coprime results to good action case

Gülı̇n Ercan

Department of Mathematics, Middle East Technical University, Ankara, Turkey

E-mail Address: ercan@metu.edu.tr

Corresponding author.

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İsmaı̇l Ş. Güloğlu

Department of Mathematics, Doğuş University, Istanbul, Turkey

E-mail Address: iguloglu@dogus.edu.tr

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, and

Enrico Jabara

Dipartimento di Filosofia, Università Ca’ Foscari di Venezia, Venice, Italy

E-mail Address: jabara@unive.it

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https://doi.org/10.1142/S021949882250222XCited by:1 (Source: Crossref)

Abstract

Let $G$ $G$ and $A$ $A$ be groups where $A$ $A$ acts on $G$ $G$ by automorphisms. We say “the action of $A$ $A$ on $G$ $G$ is good” if the equality $H = [H, B] C_{H} (B)$ $H = [H, B] C_{H} (B)$ holds for any subgroup $B$ $B$ of $A$ $A$ and for any $B$ $B$ -invariant subgroup $H$ $H$ of $G$ $G$ . 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.

Communicated by M. Lewis

Keywords:

AMSC: 20D10, 20D15, 20D45

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