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Title: A note on commutators in the group of infinite triangular matrices over a ring
Abstract:
We investigate the commutators of elements of the group UT(∞,R) of infinite unitriangular matrices over an associative ring R with 1 and a commutative group R* of invertible elements. We prove that every unitriangular matrix of a specified form is a commutator of two other unitriangular matrices. As a direct consequence we give a complete characterization of the lower central series of the group UT(∞,R) including the width of its terms with respect to basic commutators and Engel words. With an additional restriction on the ring R, we show that the derived subgroup of T(∞,R) coincides with the group UT(∞,R). The obtained results generalize the results obtained for triangular groups over a field.
Format:
Resource Identifier:
Baza Wiedzy PŚ ; oai:delibra.bg.polsl.pl:31970
Source:
Linear and Multilinear Algebra 2015 vol. 63, no. 11, s. 2301-2310
Language:
Relation:
Wydział Matematyki Stosowanej. Politechnika Śląska
Access:
Licence:
Object collections:
- Digital Library > COLLECTIONS OF PUBLICATIONS OF THE SILESIAN UNIVERSITY OF TECHNOLOGY > Publications from database "Bibliography of scientific publications of Silesian University of Technology"
Last modified:
Oct 16, 2020
In our library since:
Nov 23, 2015
Number of object content hits:
977
All available object's versions:
https://delibra.bg.polsl.pl/publication/35898
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| Edition name | Date |
|---|---|
| A note on commutators in the group of infinite triangular matrices over a ring | Oct 16, 2020 |
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