As we know, the Frattini subgroup of a finite group G can not contain a Sylow subgroup of G, but if we want to prove this, we need the Schur-Zassenhaus theorem. What I want to know is if there is a more elementary proof of this.
2026-04-11 13:15:53.1775913353
Is there a Schur-Zassenhaus-free proof that $\Phi(G)$ cannot contain a Sylow subgroup of $G$?
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