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 groups, which satisfy the so-called $(\ast )$ 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.

DOI: 10.14232/actasm-016-004-x

AMS Subject Classification (1991): 20H25, 20K30, 20G20, 15A30

Keyword(s): linear group over ring, homomorphism of matrix group, elementary subgroup over ring

Received January 26, 2016. (Registered under 4/2016.)