Isomorphisms of matrix groups over commutative rings

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 ho-momorphisms of matrix groups, which satisfy the so-called (*) condition. Such homomorphis...

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Bibliographic Details
Published in:Acta scientiarum mathematicarum (Szeged) Vol. 83; no. 1-2; pp. 113 - 123
Main Authors: Petechuk, V. M., Petechuk, J. V.
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.06.2017
Subjects:
Functional Analysis
Mathematics
Operator Theory
20G20
15A30
homomorphism of matrix group
linear group over ring
elementary subgroup over ring
20H25
20K30
ISSN:0001-6969, 2064-8316
Online Access:Get full text
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Summary: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 ho-momorphisms of matrix groups, 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.
ISSN:0001-6969
2064-8316
DOI:10.14232/actasm-016-004-x