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Acta Mathematica Vietnamica

Products of Commutators of Involutions in Skew Linear Groups

icon-email Nguyen Thi Thai Ha , Phan Hoang Nam , Tran Nam Son

Abstract

In connection with [Theorem 4.6, Linear Algebra Appl. 646, 119–131, (2022)], we show that each matrix in the commutator subgroup of the general linear group over a centrally-finite division ring D, in which each element in the commutator subgroup of D is a product of at most s commutators, can be written as a product of at most 3+3sn/2 commutators of involutions if charD2, where x, x denote the ceiling and floor functions of x, respectively. Moreover, we also present the special case when D=H, the division ring of quaternions, and an application in real group algebras.