Verbal subgroups in the group of triangular matrices over field of characteristic 0

Agnieszka Bier

doi:10.1016/j.jalgebra.2008.10.006

Verbal subgroups in the group of triangular matrices over field of characteristic 0

Agnieszka Bier

Department of Mathematics (RMS/RMS1)

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

10 Citations (Scopus)

Abstract

In this paper we describe the verbal subgroups of groups UT_n (K) and T_n (K), which are the groups of, respectively, unitriangular and triangular matrices over field K of characteristic 0. We prove that every verbal subgroup of UT_n (K) coincides with a term of the lower central series of the group and that every verbal subgroup V (T_n (K)) either is of the form V (K) ṡ UT_n (K) or coincides with a verbal subgroup of UT_n (K). We also describe the width of these verbal subgroups and make a few remarks regarding the groups of infinite triangular matrices.

Original language	English
Pages (from-to)	483-494
Number of pages	12
Journal	Journal of Algebra
Volume	321
Issue number	2
DOIs	https://doi.org/10.1016/j.jalgebra.2008.10.006
Publication status	Published - 15 Jan 2009

Keywords

Central series
Nilpotent group
The group of triangular matrices
Verbal subgroup
Verbal width

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2008.10.006

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abstract = "In this paper we describe the verbal subgroups of groups UTn (K) and Tn (K), which are the groups of, respectively, unitriangular and triangular matrices over field K of characteristic 0. We prove that every verbal subgroup of UTn (K) coincides with a term of the lower central series of the group and that every verbal subgroup V (Tn (K)) either is of the form V (K) ṡ UTn (K) or coincides with a verbal subgroup of UTn (K). We also describe the width of these verbal subgroups and make a few remarks regarding the groups of infinite triangular matrices.",

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author = "Agnieszka Bier",

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AU - Bier, Agnieszka

PY - 2009/1/15

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N2 - In this paper we describe the verbal subgroups of groups UTn (K) and Tn (K), which are the groups of, respectively, unitriangular and triangular matrices over field K of characteristic 0. We prove that every verbal subgroup of UTn (K) coincides with a term of the lower central series of the group and that every verbal subgroup V (Tn (K)) either is of the form V (K) ṡ UTn (K) or coincides with a verbal subgroup of UTn (K). We also describe the width of these verbal subgroups and make a few remarks regarding the groups of infinite triangular matrices.

AB - In this paper we describe the verbal subgroups of groups UTn (K) and Tn (K), which are the groups of, respectively, unitriangular and triangular matrices over field K of characteristic 0. We prove that every verbal subgroup of UTn (K) coincides with a term of the lower central series of the group and that every verbal subgroup V (Tn (K)) either is of the form V (K) ṡ UTn (K) or coincides with a verbal subgroup of UTn (K). We also describe the width of these verbal subgroups and make a few remarks regarding the groups of infinite triangular matrices.

KW - Central series

KW - Nilpotent group

KW - The group of triangular matrices

KW - Verbal subgroup

KW - Verbal width

UR - https://www.scopus.com/pages/publications/57349199718

U2 - 10.1016/j.jalgebra.2008.10.006

DO - 10.1016/j.jalgebra.2008.10.006

M3 - Article

AN - SCOPUS:57349199718

SN - 0021-8693

VL - 321

SP - 483

EP - 494

JO - Journal of Algebra

JF - Journal of Algebra

IS - 2

ER -

Verbal subgroups in the group of triangular matrices over field of characteristic 0

Abstract

Keywords

ASJC Scopus subject areas

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