Isomorphisms of matrix groups over commutative rings

Abstract

Abstract. We give a description of the isomorphism classes of matrix groups over commutative rings with 1 and that have dimension more than 3 and containing the group of elementary transvections. We characterize those homomorphisms of matrix groupe, which satisfy the so-called (*) condition. Such homomorphisms can be constructed with the help of the standard homomorphism. We apply the characterization obtained to the description of the above class of matrix groups.