(* Representation kernel, and faithful representations. *)
Definition rker := rstab 1%:M.
Canonical rker_group := Eval hnf in [group of rker].

(* Specifications: *)
Lemma rkerP x : reflect (x \in G /\ rG x = 1%:M) (x \in rker).
Lemma rker_normal : rker <| G.
Lemma rker_linear : n = 1%N -> G^`(1)%g \subset rker.
Definition rcenter := [set g in G | is_scalar_mx (rG g)].