A note on commutators in the group of infinite triangular matrices over a ring

DOI10.1080/03081087.2014.1003529zbMath1331.20068OpenAlexW2032249600MaRDI QIDQ3455683

Waldemar Hołubowski, Agnieszka Bier

Publication date: 11 December 2015

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: http://delibra.bg.polsl.pl/Content/31970/REPO_35898_-_A-note-on-commutator_0000.pdf

zbMATH Keywords

lower central seriesderived subgroupcommutator widthsVershik-Kerov groupunitriangular matricesinfinite triangular matrix groups

Mathematics Subject Classification ID

Factorization of matrices (15A23) Other matrix groups over rings (20H25) Derived series, central series, and generalizations for groups (20F14) Commutator calculus (20F12)

Related Items

THE p-ZASSENHAUS FILTRATION OF A FREE PROFINITE GROUP AND SHUFFLE RELATIONS ⋮ Involution widths of skew linear groups generated by involutions ⋮ Massey products in Galois cohomology and the elementary type conjecture ⋮ On a generalized Jordan form of an infinite upper triangular matrix ⋮ Normal subgroups in the group of column-finite infinite matrices

Cites Work

• Commutator subgroup of Vershik-Kerov group.
• On one property of normal subgroups of \(\mathrm{UT}_\infty(R)\).
• Counting irreducible representations of large degree of the upper triangular groups.
• Counting characters of small degree in upper unitriangular groups.
• Rings which are generated by their units
• The group of units in a compact ring
• Semiperfect rings with abelian group of units
• On an infinite-dimensional group over a finite field
• Two classes of rings generated by their units
• The upper triangular group and operations in algebraic K-theory
• On solvability of Engel equations in the group of triangular matrices over a field.
• Commutators and powers of infinite unitriangular matrices.
• Isomorphisms of the unitriangular groups and associated Lie rings for the exceptional dimen\-sions.
• The lower central series of subgroups of the Vershik-Kerov group.
• D.C.C. rings with a cyclic group of units
• Bijective maps of infinite triangular and unitriangular matrices preserving commutators
• THE WIDTH OF VERBAL SUBGROUPS IN THE GROUP OF UNITRIANGULAR MATRICES OVER A FIELD
• Inverses of Matrices $\{a_{ij}\}$ which Satisfy $a_{ij} = 0$ for $j > i+p$.
• RIGHT SELF-INJECTIVE RINGS IN WHICH EVERY ELEMENT IS A SUM OF TWO UNITS
• An inverse matrix of an upper triangular matrix can be lower triangular

This page was built for publication: A note on commutators in the group of infinite triangular matrices over a ring