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articleNo Access
Extensions of several coprime results to good action case
Journal of Algebra and Its Applications29 Jul 2021
Preview 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.

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