“…For the converse, since the groupḠ = G/H is linear, there is an homomorphism ϑ : G −→ R to a linear group R with Kerϑ ≤ H. On the other hand the linearity ofḠ = G/H implies the residually finiteness of it, but the correspondingH = (K/H)Ḡ is trivial. Therefore, by the main Theorem in [1] the groupD = D/H must be finite, which, by the Theorem 2 in [2], implies that there exists a finitely generated abelian group X such that K ≤ X and an automorphismφ of X withφ| A = ϕ. Now the obvious homomorphism ̺ : G −→ X ⋊ φ is an embedding on K, so Ker̺ ∩ K = 1.…”