Section CentHom.
Variable f : 'M[R]_n.
Definition rcent := [set x in G | f *m rG x == rG x *m f].
Canonical rcent_group := Group rcent_group_set.
Definition centgmx := G \subset rcent.
End CentHom.
(* Representation kernel, and faithful representations. *)
Definition rker := rstab 1%:M.
Canonical rker_group := Eval hnf in [group of rker].

Lemma rkerP x : reflect (x \in G /\ rG x = 1%:M) (x \in rker).