Section Defs.
Variable gT : finGroupType.
Definition center (A : {set gT}) := 'C_A(A).
Canonical center_group (G : {group gT}) : {group gT} :=
Eval hnf in [group of center G].
End Defs.
Arguments center {gT} A%g.
Notation "''Z' ( A )" := (center A) : group_scope.
Notation "''Z' ( H )" := (center_group H) : Group_scope.

Lemma cyclic_factor_abelian H G :
H \subset 'Z(G) -> cyclic (G / H) -> abelian G.