Expansive automorphisms of totally disconnected, locally compact groups

Article Type

Research Article

Publication Title

Journal of Group Theory

Abstract

We study topological automorphisms a of a totally disconnected, locally compact group G which are expansive in the sense that ∩ n∈ℤ an (U) = {1} for some identity neighbourhood U ⊆ G. Notably, we prove that the automorphism induced by an expansive automorphism a on a quotient group G/N modulo an a-stable closed normal subgroup N is always expansive. Further results involve the contraction groups Ua := {g ∈ G : An(g) → 1 as n → ∞}. If a is expansive, then UaUa-1 is an open identity neighbourhood in G. We give examples where UaUa-1 fails to be a subgroup. However, UaUa-1 is an a-stable, nilpotent open subgroup of G if G is a closed subgroup of GLn(ℚp). Further results are devoted to the divisible and torsion parts of Ua, and to the so-called "nub" nub(a) = Ua\ ∩ Ua-1 of an expansive automorphism.

First Page

589

Last Page

619

DOI

10.1515/jgth-2016-0051

Publication Date

5-1-2017

Comments

Open Access, Green

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