S$\Phi$-supplemented and coprime action in finite groups

Abstract

 An $A$-invariant subgroup $H$ of $G$ is said to be $AS\Phi$-supplemented in $G$ if there exists an $A$-invariant normal subgroup $T$ of $G$ such that $G=HT$ and $ H\cap T\le \Phi(H)$, where $\Phi(H)$ is the Frattini subgroup of $H$. In this paper, we study $S\Phi$-supplement in the coprime action setting so as to obtain several $p$-nilpotency criteria in terms of certain subsets of maximal invariant subgroups of its Sylow subgroups.

Keywords

• Coprime action
• SΦ-supplemented
• p-nilpotency

References

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