proposition: Lemma Q8_extraspecial : extraspecial 'Q_8.
proof: Proof. have gt32: 3 > 2 by []; have isoQ: 'Q_8 \isog 'Q_(2 ^ 3) by apply: isog_refl. have [[x y] genQ _] := generators_quaternion gt32 isoQ. have [_ [defQ' defPhiQ _ _]] := quaternion_structure gt32 genQ isoQ. case=> defZ oZ _ _ _ _ _; split; last by rewrite oZ. by split; rewrite ?defPhiQ defZ. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(choice fintype bigop finset prime binomial) mathcomp(fingroup morphism perm automorphism presentation) mathcomp(quotient action commutator gproduct gfunctor) mathcomp(ssralg finalg zmodp cyclic pgroup center gseries) mathcomp(nilpotent sylow abelian finmodule matrix maximal) mathcomp(extremal)