Section Cycles.
(* Elementary properties of cycles and order, needed in perm.v.  *)
(* More advanced results on the structure of cyclic groups will  *)
(* be given in cyclic.v.                                         *)
Variable gT : finGroupType.
Implicit Types x y : gT.
Implicit Types G : {group gT}.

Lemma expg_mod p k x : x ^+ p = 1 -> x ^+ (k %% p) = x ^+ k.