logo_acta

Acta Mathematica Vietnamica

On the Diagonal Subgroup of the Special Linear Group Over a Division Ring

icon-email Bui Xuan Hai

Abstract

Let K be a division ring with center Z(K), and n a positive integer. Let SL(n,K) be the special linear group of degree n over K and SD(n,K) its subgroup consisting of all diagonal matrices whose Dieudonne’s determinant is 1. We prove that SD(n,K) is weakly pronormal, but not pronormal in SL(n,K) provided either Z(K) is an infinite field in case n3 or Z(K) is a finite field containing at least seven elements in case n5.