proposition: Lemma p_rank_Ohm1 p G : 'r_p('Ohm_1(G)) = 'r_p(G).
proof: Proof. apply/eqP; rewrite eqn_leq p_rankS ?Ohm_sub //. apply/bigmax_leqP=> E /setIdP[sEG abelE]. by rewrite (bigmax_sup E) // inE -{1}(Ohm1_id abelE) OhmS. 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)