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  • Author: George A. Willis x
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Abstract

Let G be a totally disconnected, locally compact group admitting a contractive automorphism α. We prove a Jordan-Hölder theorem for series of α-stable closed subgroups of G, classify all possible composition factors and deduce consequences for the structure of G.

Abstract

We introduce the notion of the k-closure of a group of automorphisms of a locally finite tree, and give several examples of the construction. We show that the k-closure satisfies a new property of automorphism groups of trees that generalises Tits' Property P. We prove that, apart from some degenerate cases, any non-discrete group acting on a tree with this property contains an abstractly simple subgroup.