On the local Frattini subgroup of a finite group

David G. Costanzo

Let $G$ be a finite group and let $\pi (G)$ be the set of prime divisors of $|G|$. For each $p\in \pi (G)$, choose a Sylow $p$-subgroup $G_p$ of $G$. The subgroup $Ψ(G)= \prod_{p\in π(G)…