Configuration of subgroups in the special linear group over a skew field with infinite center

Abstract

Let T be a skew field with infinite center, let Γ be the special linear group over T of degree ≥ 3, and let Δ be the subgroup of diagonal matrices with unit Dieudonee determinant. It is proved that for each intermediate subgroup H, Δ ≤ H ≤ Γ, there exists a net σ of order n such that Γ(σ ≤ H ≤ N(σ).