On one property of normal subgroups of UT∞ (R)

Roksana Słowik

doi:10.1016/j.laa.2012.06.001

On one property of normal subgroups of ^UT∞ (R)

Roksana Słowik

Department of Mathematics (RMS/RMS1)

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

We examine the group of infinite unitriangular matrices. We show that to find a normal subgroup of ^UT∞(R) for any unital ring R, it suffices to examine properties of matrices in this group having nonzero entries only on some first diagonals. We use this result to find the commutator subgroup of the group of all triangular matrices. We also describe the commutator subgroup of the Vershik-Kerov group.

Original language	English
Pages (from-to)	2300-2307
Number of pages	8
Journal	Linear Algebra and Its Applications
Volume	437
Issue number	9
DOIs	https://doi.org/10.1016/j.laa.2012.06.001
Publication status	Published - 1 Nov 2012

Keywords

Commutator subgroup
Infinite unitriangular matrices
Normal subgroup

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

Access to Document

10.1016/j.laa.2012.06.001

Cite this

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abstract = "We examine the group of infinite unitriangular matrices. We show that to find a normal subgroup of UT∞(R) for any unital ring R, it suffices to examine properties of matrices in this group having nonzero entries only on some first diagonals. We use this result to find the commutator subgroup of the group of all triangular matrices. We also describe the commutator subgroup of the Vershik-Kerov group.",

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N2 - We examine the group of infinite unitriangular matrices. We show that to find a normal subgroup of UT∞(R) for any unital ring R, it suffices to examine properties of matrices in this group having nonzero entries only on some first diagonals. We use this result to find the commutator subgroup of the group of all triangular matrices. We also describe the commutator subgroup of the Vershik-Kerov group.

AB - We examine the group of infinite unitriangular matrices. We show that to find a normal subgroup of UT∞(R) for any unital ring R, it suffices to examine properties of matrices in this group having nonzero entries only on some first diagonals. We use this result to find the commutator subgroup of the group of all triangular matrices. We also describe the commutator subgroup of the Vershik-Kerov group.

KW - Commutator subgroup

KW - Infinite unitriangular matrices

KW - Normal subgroup

UR - https://www.scopus.com/pages/publications/84864765323

U2 - 10.1016/j.laa.2012.06.001

DO - 10.1016/j.laa.2012.06.001

M3 - Article

AN - SCOPUS:84864765323

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EP - 2307

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

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