Covering Numbers with Involutions in Decomposing Infinite Matrices

Truong Huu Dung; Nguyen Thi Thai Ha

Vol. 30 No. 1 (2025)

Regular Articles

Covering Numbers with Involutions in Decomposing Infinite Matrices

Published 2025-03-11

Truong Huu Dung
Nguyen Thi Thai Ha

Truong Huu Dung
Dong Nai University

Nguyen Thi Thai Ha
Campus in Ho Chi Minh City, University of Transport and Communications

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Abstract

Let $D$ be a division ring. The aim of this paper is to explore the problem of decomposing an infinite matrix over $D$ into a product of involutions and a product of commutators of involutions within the context of covering numbers. Specifically, we focus on decomposing matrices in the commutator subgroup $\mathrm{SL}_{VK,\infty}(D)$ of the Vershik–Kerov group and in the subgroup $\mathrm{SL}_{\infty}(D)$ of the stable general linear group $\mathrm{GL}_{\infty}(D)$.

Keywords

division ring, matrix decomposition, commutator, involution, infinite matrix

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