proposition: Lemma extraspecial_nonabelian G : extraspecial G -> ~~ abelian G.
proof: Proof. case=> [[_ defG'] oZ]; rewrite /abelian (sameP commG1P eqP). by rewrite -derg1 defG' -cardG_gt1 prime_gt1. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(div fintype finfun bigop finset prime binomial) mathcomp(fingroup morphism perm automorphism quotient) mathcomp(action commutator gproduct gfunctor ssralg) mathcomp(countalg finalg zmodp cyclic pgroup center gseries) mathcomp(nilpotent sylow abelian finmodule)