"Expansive automorphisms of totally disconnected, locally compact group" by Helge Glöckner and C. R.E. Raja
 

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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