proposition: Lemma rank_cycle (x : gT) : 'r(<[x]>) = (x != 1).
proof: Proof. have [->|ntx] := eqVneq x 1; first by rewrite cycle1 rank1. apply/eqP; rewrite eqn_leq rank_gt0 cycle_eq1 ntx andbT. by rewrite -grank_abelian ?cycle_abelian //= -(cards1 x) grank_min. 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)