- Title
- Approximating simple locally compact groups by their dense locally compact subgroups
- Creator
- Caprace, Pierre-Emmanuel; Reid, Colin; Wesolek, Phillip
- Relation
- ARC.DP120100996 http://purl.org/au-research/grants/arc/DP120100996
- Relation
- International Mathematics Research Notices Vol. 2021, Issue 7, p. 5037-5110
- Publisher Link
- http://dx.doi.org/10.1093/imrn/rny298
- Publisher
- Oxford University Press
- Resource Type
- journal article
- Date
- 2021
- Description
- The class S of totally disconnected locally compact (tdlc) groups that are non-discrete, compactly generated, and topologically simple contains many compelling examples. In recent years, a general theory for these groups, which studies the interaction between the compact open subgroups and the global structure, has emerged. In this article, we study the non-discrete tdlc groups H that admit a continuous embedding with dense image into some G ∈ S that is, we consider the dense locally compact subgroups of groups G ∈ S. We identify a class ℛ of almost simple groups that properly contains S and is moreover stable under passing to a non-discrete dense locally compact subgroup. We show that ℛ enjoys many of the same properties previously obtained for S and establish various original results for ℛ that are also new for the subclass S, notably concerning the structure of the local Sylow subgroups and the full automorphism group.
- Subject
- groups; locally compact; continuous embedding; Sylow
- Identifier
- http://hdl.handle.net/1959.13/1445342
- Identifier
- uon:42564
- Identifier
- ISSN:1073-7928
- Language
- eng
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