Finite Groups Embeddable in Division Rings

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...

On nest modules of matrices over division rings

Let $ m , n in mathbb{N}$, $D$ be a division ring, and $M_{m times n}(D)$ denote the bimodule of all $m times n$ matrices with entries from $D$. First, we characterize one-sided submodules of $M_{m times n}(D)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $D$. Next, we introduce the notion of a nest module of matrices with entries from $D$. We ...

On One-Sided Ideals of Rings of Linear Transformations

On Groups That Have Normal Forms Computable in Logspace Murray Elder, Gillian Elston, and Gretchen Ostheimer

We consider the class of finitely generated groups which have a normal form computable in logspace. We prove that the class of such groups is closed under passing to finite index subgroups, direct products, wreath products, and certain free products and infinite extensions, and includes the solvable Baumslag-Solitar groups, as well as non-residually finite (and hence nonlinear) examples. We def...

Uniform embeddability of relatively hyperbolic groups

Let G be a finitely generated group which is hyperbolic relative to a finite family fH1; . . . ;Hng of subgroups. We prove that G is uniformly embeddable in a Hilbert space if and only if each subgroup Hi is uniformly embeddable in a Hilbert space.