Solvable Linear Groups over Division Rings

Triangulaizability of Algebras Over Division Rings

Groups definable in ordered vector spaces over ordered division rings

Let M = 〈M, +, <, 0, {λ}λ∈D〉 be an ordered vector space over an ordered division ring D, and G = 〈G,⊕, eG〉 an n-dimensional group definable in M. We show that if G is definably compact and definably connected with respect to t-topology, then it is definably isomorphic to a ‘definable quotient group’ U/L, for some convex W -definable subgroup U of 〈Mn, +〉 and a lattice L of rank n. As two conseq...

Undistorted Solvable Linear Groups

We discuss distortion of solvable linear groups over a locally compact field and provide necessary and sufficient conditions for a subgroup to be undistorted when the field is of characteristic zero.

Triangularization over finite-dimensional division rings using the reduced trace

In this paper we study triangularization of collections of matrices whose entries come from a finite-dimensional division ring. First, we give a generalization of Guralnick's theorem to the case of finite-dimensional division rings and then we show that in this case the reduced trace function is a suitable alternative for trace function by presenting two triangularization results. The first one...

Group Rings with Solvable «-engel Unit Groups'

Let KG be the group ring of a group G over a field of characteristic p > 0, p ^ 2, 3. Suppose G contains no element of order p (if p > 0). Group algebras KG with unit group U(KG) solvable and n-Engel are characterized. Let ATG be the group ring of a group G over a field K of characteristic p > 0 and let U(KG) denote its group of units. Several authors including Bateman [1], Bateman and Coleman ...