Normal Subgroup Structure of Totally Disconnected Locally Compact Groups
The present article is a summary of joint work of the author and Phillip Wesolek on the normal subgroup structure of totally disconnected locally compact second-countable (t.d.l.c.s.c.) groups. The general strategy is as follows: We obtain normal series for a t.d.l.c.s.c. group in which each factor is ‘small’ or a non-abelian chief factor; we show that up to a certain equivalence relation (called association), a given non-abelian chief factor can be inserted into any finite normal series; and we obtain restrictions on the structure of chief factors, such that the restrictions are invariant under association. Some limitations of this strategy and ideas for future work are also discussed.
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The author is an ARC DECRA fellow; this article is based on research supported in part by ARC Discovery Project DP120100996. I thank Pierre-Emmanuel Caprace and Phillip Wesolek for their very helpful feedback on the presentation of this material. I also thank George Willis for his insights on contraction groups.
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