proposition: Lemma plength1_Sylow_prod : K * S = 'O_{p^',p}(G).
proof: Proof. by rewrite -quotientK 1?(eq_Hall_pcore sylGbp) ?quotient_pHall //= /K -pseries1. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrfun ssrbool eqtype ssrnat seq div fintype finset) mathcomp(prime fingroup morphism automorphism quotient gproduct gfunctor) mathcomp(cyclic center commutator pgroup nilpotent sylow abelian hall) mathcomp(maximal) odd_order(BGsection1 BGappendixAB)