Object

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:

application/pdf

Resource Identifier:

Baza „Dorobek” – nr opisu: 0000103046 ; oai:repolis.bg.polsl.pl:31970

Source:

Linear and Multilinear Algebra 2015 vol. 63, no. 11, s. 2301-2310

Language:

eng

Relation:

Wydział Matematyki Stosowanej. Politechnika Śląska

Access:

zasób dostępny bez ograniczeń

Licence:

CC BY 3.0

Object collections:

Last modified:

Nov 30, 2015

In our library since:

Nov 23, 2015

Number of object content hits:

513

All available object's versions:

https://repolis.bg.polsl.pl/publication/35898

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