proposition: Lemma Ohm1_cent_max G E p : E \in 'E*_p(G) -> p.-group G -> 'Ohm_1('C_G(E)) = E.
proof: Proof. move=> EpmE pG; have [G1 | ntG]:= eqsVneq G 1. case/pmaxElemP: EpmE; case/pElemP; rewrite G1 => /trivgP-> _ _. by apply/trivgP; rewrite cent1T setIT Ohm_sub. have [p_pr _ _] := pgroup_pdiv pG ntG. by rewrite (OhmE 1 (pgroupS (subsetIl G _) pG)) (pmaxElem_LdivP _ _) ?genGid. 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)