End AbelianQuotient.
Section Similarity.
Variables (gT : finGroupType) (G : {group gT}).
Local Notation reprG := (mx_representation F G).
Variant mx_rsim n1 (rG1 : reprG n1) n2 (rG2 : reprG n2) : Prop :=
MxReprSim B of n1 = n2 & row_free B
& forall x, x \in G -> rG1 x *m B = B *m rG2 x.

Lemma mx_rsim_trans n1 n2 n3
(rG1 : reprG n1) (rG2 : reprG n2) (rG3 : reprG n3) :
mx_rsim rG1 rG2 -> mx_rsim rG2 rG3 -> mx_rsim rG1 rG3.