ite (Frobenius_autB_comm _ (commr1 _)) Frobenius_aut1.
by rewrite -[_ (rG z)](repr_mxX rG) // -ozp expg_order repr_mx1 subrr unitr0.
Qed.Hypothesis nEG : G \subset 'N(E).
Local Notation r := (abelem_mx nEG).ite rVabelemD rVabelemZ conjMg conjXg.
by rewrite abelem_rV_M ?abelem_rV_X ?groupX ?memJ_norm // natr_Zp.=> Gx; rewrite /= mul_rV_lin1 /= /abelem_mx_fun subgK //.
by rewrite abelem_rV_K // memJ_norm // (subsetP nEG).
Qed.rewrite rowE -row1 rVabelemJmx // conjg1.
by rewrite !rowE mulmxA !rVabelemJmx ?groupM // conjgM.Local Notation rG := (abelem_repr nEG).

Qed.