proposition: Remark norm_sigma_Sylow p P : p \in \sigma(M) -> p.-Sylow(M) P -> 'N(P) \subset M.
proof: Proof. case/exists_inP=> Q sylQ sNPM sylP. by case: (Sylow_trans sylQ sylP) => m mM ->; rewrite normJ conj_subG. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrbool ssrfun eqtype ssrnat seq div path fintype) mathcomp(bigop finset prime fingroup morphism perm automorphism quotient) mathcomp(action gproduct gfunctor pgroup cyclic center commutator) mathcomp(gseries nilpotent sylow abelian maximal hall) odd_order(BGsection1 BGsection3 BGsection4 BGsection5 BGsection6) odd_order(BGsection7 BGsection9)