Related papers: Locally normal subgroups of simple locally compact…
We use the structure lattice, introduced in Part I, to undertake a systematic study of the class $\mathscr S$ consisting of compactly generated, topologically simple, totally disconnected locally compact groups that are non-discrete. Given…
Let G be a totally disconnected, locally compact group. A closed subgroup of G is locally normal if its normaliser is open in G. We begin an investigation of the structure of the family of closed locally normal subgroups of G. Modulo…
It is shown that a closed solvable subgroup of a connected Lie group is compactly generated. In particular, every discrete solvable subgroup of a connected Lie group is finitely generated. Generalizations to locally compact groups are…
We describe the global structure of totally disconnected locally compact groups having a linear open compact subgroup. Among the applications, we show that if a non-discrete, compactly generated, topologically simple, totally disconnected…
A locally normal subgroup in a topological group is a subgroup whose normaliser is open. In this paper, we provide a detailed description of the large-scale structure of closed locally normal subgroups of complete Kac-Moody groups over…
We establish a general normal subgroup theorem for commensurators of lattices in locally compact groups. While the statement is completely elementary, its proof, which rests on the original strategy of Margulis in the case of higher rank…
We study locally compact contractive local groups, that is, locally compact local groups with a contractive pseudo-automorphism. We prove that if such an object is locally connected, then it is locally isomorphic to a Lie group. We also…
The aim of this note is to insert in the literature some easy but apparently not widely known facts about morphisms of locally compact groups, all of which are concerned with the openness of the morphism.
We present a contribution to the structure theory of locally compact groups. The emphasis is on compactly generated locally compact groups which admit no infinite discrete quotient. It is shown that such a group possesses a characteristic…
We introduce and explore a natural rank for totally disconnected locally compact groups called the bounded conjugacy rank. This rank is shown to be a lattice invariant for lattices in sigma compact totally disconnected locally compact…
Automorphism groups of locally finite trees provide a large class of examples of simple totally disconnected locally compact groups. It is desirable to understand the connections between the global and local structure of such a group.…
We prove that the lattice of normal subgroups of ultraproducts of compact simple non-abelian groups is distributive. In the case of ultraproducts of finite simple groups or compact connected simple Lie groups of bounded rank the set of…
We introduce the notion of soficity for locally compact groups and list a number of open problems.
We introduce the notion of commability between locally compact groups, namely the equivalence relation generated by cocompact inclusions and quotients by compact normal subgroups. We give a classification of focal hyperbolic locally compact…
We describe locally compact groups which are separably categorical metric structures. The paper extends (and corrects) Section 3 of the paper A.Ivanov, "Locally compact groups and continuous logic", arXiv: 1206.5473
An elementary proof is given for the fact that every locally compact subsemigroup of a compact topological group is a closed subgroup. A sample consequence is that every commutative cancellative pseudocompact locally compact Hausdorff…
The aim of this work is to understand some of the asymptotic properties of sequences of lattices in a fixed locally compact group. In particular we will study the asymptotic growth of the Betti numbers of the lattices renormalized by the…
Locally solid Riesz spaces have been widely investigated in the past several decades; but locally solid topological lattice-ordered groups seem to be largely unexplored. The paper is an attempt to initiate a relatively systematic study of…
We construct locally compact groups with no non-trivial Invariant Random Subgroups and no non-trivial Uniformly Recurrent Subgroups.
We show that the group of type-preserving automorphisms of any irreducible semi-regular thick right-angled building is abstractly simple. When the building is locally finite, this gives a large family of compactly generated (abstractly)…