proposition: Lemma plength1_pseries2_quo G : p.-length_1 G = p^'.-group (G / 'O_{p^', p}(G)).
proof: Proof. rewrite /plength_1 eqEsubset pseries_sub lastI pseries_rcons /=. rewrite -sub_quotient_pre ?gFnorm //. by apply/idP/idP=> pl1G; rewrite ?pcore_pgroup_id ?(pgroupS pl1G) ?pcore_pgroup. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrbool ssrfun eqtype ssrnat seq path div fintype) mathcomp(bigop prime binomial finset fingroup morphism perm automorphism) mathcomp(quotient action gproduct gfunctor commutator) mathcomp(ssralg finalg zmodp cyclic center pgroup finmodule gseries) mathcomp(nilpotent sylow abelian maximal hall extremal) mathcomp(matrix mxalgebra mxrepresentation mxabelem)