- Title
- Distal actions on coset spaces in totally disconnected locally compact groups
- Creator
- Reid, Colin D.
- Relation
- ARC.DP120100996 http://purl.org/au-research/grants/arc/DP120100996
- Relation
- Journal of Topology and Analysis Vol. 12, Issue 2, p. 491-532
- Publisher Link
- http://dx.doi.org/10.1142/S1793525319500523
- Publisher
- World Scientific Publishing
- Resource Type
- journal article
- Date
- 2020
- Description
- Let G be a totally disconnected locally compact (t.d.l.c.) group and let H be an equicontinuously (for example, compactly) generated group of automorphisms of G. We show that every distal action of H on a coset space of G is a SIN action, with the small invariant neighborhoods arising from open H-invariant subgroups. We obtain a number of consequences for the structure of the collection of open subgroups of a t.d.l.c. group. For example, it follows that for every compactly generated subgroup K of G, there is a compactly generated open subgroup E of G such that K = E and such that every open subgroup of G containing a finite index subgroup of K contains a finite index subgroup of E. We also show that for a large class of closed subgroups L of G (including for instance all closed subgroups L such that L is an intersection of subnormal subgroups of open subgroups), every compactly generated open subgroup of L can be realized as L ? O for an open subgroup of G.
- Subject
- totally disconnected locally compact groups; coset spaces; automorphisms; open subgroups
- Identifier
- http://hdl.handle.net/1959.13/1440529
- Identifier
- uon:41169
- Identifier
- ISSN:1793-5253
- Language
- eng
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