proposition: Lemma exponent_Hall pi G H : pi.-Hall(G) H -> exponent H = (exponent G)`_pi.
proof: Proof. move=> hallH; have [sHG piH _] := and3P hallH. rewrite -(partn_exponentS sHG) -?(card_Hall hallH) ?part_pnat_id //. by apply: pnat_dvd piH; apply: exponent_dvdn. 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)