proposition: Lemma p_rankElem_max p A : 'E_p^('r_p(A))(A) \subset 'E*_p(A).
proof: Proof. apply/subsetP=> E /setIdP[EpE dimE]. apply/pmaxElemP; split=> // F EpF sEF; apply/eqP. have pF: p.-group F by case/pElemP: EpF => _ /and3P[]. have pE: p.-group E by case/pElemP: EpE => _ /and3P[]. rewrite eq_sym eqEcard sEF dvdn_leq // (card_pgroup pE) (card_pgroup pF). by rewrite (eqP dimE) dvdn_exp2l // logn_le_p_rank. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path choice) mathcomp(div fintype finfun bigop finset prime binomial) mathcomp(fingroup morphism perm automorphism action) mathcomp(quotient gfunctor gproduct ssralg countalg finalg zmodp) mathcomp(cyclic pgroup gseries nilpotent sylow)