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Chief series in locally compact groups Reid, Colin
Description
I will be talking about joint work with Phillip Wesolek. A chief factor of a topological group $G$ is a factor $K/L$, where $K$ and $L$ are closed normal subgroups such that no closed normal subgroup of $G$ lies strictly between $K$ and $L$. We show that a compactly generated locally compact group admits an 'essentially chief series', that is, a finite normal series in which each of the factors is compact, discrete or a chief factor. In the totally disconnected case, the proof is based on the fact that $G$ acts vertex-transitively on a locally finite connected graph with compact open stabilizers. I will also indicate why totally disconnected chief factors can have a complicated normal subgroup structure as groups in their own right, in contrast to semisimple groups.
Item Metadata
Title |
Chief series in locally compact groups
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2016-11-17T17:28
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Description |
I will be talking about joint work with Phillip Wesolek. A chief factor of a topological group $G$ is a factor $K/L$, where $K$ and $L$ are closed normal subgroups such that no closed normal subgroup of $G$ lies strictly between $K$ and $L$. We show that a compactly generated locally compact group admits an 'essentially chief series', that is, a finite normal series in which each of the factors is compact, discrete or a chief factor. In the totally disconnected case, the proof is based on the fact that $G$ acts vertex-transitively on a locally finite connected graph with compact open stabilizers. I will also indicate why totally disconnected chief factors can have a complicated normal subgroup structure as groups in their own right, in contrast to semisimple groups.
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Extent |
32 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: University of Newcastle
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Series | |
Date Available |
2017-05-15
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0347517
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Postdoctoral
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Rights URI | |
Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International