Locally compact wreath products

Abstract

Wreath products of non-discrete locally compact groups are usually not locally compact groups, nor even topological groups. We introduce a natural extension of the wreath product construction to the setting of locally compact groups. As an application, we disprove a conjecture of Trofimov, constructing compactly generated locally compact groups of intermediate growth without nontrivial compact normal subgroups.

28 pages

References in corpus (6)

• Metric geometry of locally compact groups
• Elementary totally disconnected locally compact groups
• Amenable uniformly recurrent subgroups and lattice embeddings
• Lattices in amenable groups
• Future directions in locally compact groups
• Abstract quotients of profinite groups, after Nikolov and Segal

Cited by in corpus (6)

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• Ozawa's class $\mathcal{S}$ for locally compact groups and unique prime factorization
• Simple groups and irreducible lattices in wreath products