proposition: Lemma plength1_nonprime G : ~~ prime p -> p.-length_1 G.
proof: Proof. move=> not_p_pr; rewrite plength1_p'group // p'groupEpi mem_primes. by rewrite (negPf not_p_pr). Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrbool ssrfun eqtype ssrnat seq path div fintype) mathcomp(bigop prime binomial finset fingroup morphism perm automorphism) mathcomp(quotient action gproduct gfunctor commutator) mathcomp(ssralg finalg zmodp cyclic center pgroup finmodule gseries) mathcomp(nilpotent sylow abelian maximal hall extremal) mathcomp(matrix mxalgebra mxrepresentation mxabelem)