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.)
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