Let G be a locally compact topological group. A lattice in G is a discrete subgroup Γ such that Γ\G carries a finite G–invariant measure, and Γ is uniform or cocompact if Γ\G is compact. Lattices in Lie groups have been well-studied. See, for example, Raghunathan [48], and for open problems the section on “Lattices in Lie groups” in this wiki. Much less is known about lattices in other locally ...

let $g$ be a group and $x in g$‎. ‎the cyclicizer of $x$ is defined to be the subset $cyc(x)=lbrace y in g mid langle x‎, ‎yrangle ; {rm is ; cyclic} rbrace$‎. ‎$g$ is said to be a tidy group if $cyc(x)$ is a subgroup for all $x in g$‎. ‎we call $g$ to be a c-tidy group if $cyc(x)$ is a cyclic subgroup for all $x in g setminus k(g)$‎, ‎where $k(g)$ is the intersection of all the cyclicizers in ...

We give two applications of the recent classification of locally finite simple finitary skew linear groups. We show that certain irreducible finitary skew linear groups of infinite dimension, generate the variety of all groups and have infinite Prüfer rank.