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}.
Arguments normP {x A}.
Canonical normaliser_group A := group (group_set_normaliser A).
Arguments normsP {A B}.

Lemma memJ_norm x y A : x \in 'N(A) -> (y ^ x \in A) = (y \in A).