Section IsoCyclic.
Variables gT rT : finGroupType.
Implicit Types (G H : {group gT}) (M : {group rT}).

(* Specifications: *)
Lemma injm_cyclic G H (f : {morphism G >-> rT}) :
'injm f -> H \subset G -> cyclic (f @* H) = cyclic H.
Lemma isog_cyclic G M : G \isog M -> cyclic G = cyclic M.
Lemma injm_generator G H (f : {morphism G >-> rT}) x :
'injm f -> x \in G -> H \subset G ->
generator (f @* H) (f x) = generator H x.