Limits of contraction groups and the tits core

Title: Limits of contraction groups and the tits core
Creator: Caprace, Pierre-Emmanuel; Reid, Colin D.; Willis, George A.
Relation: ARC.DP120100996 & ARC.DP0984342 http://purl.org/au-research/grants/arc/DP120100996
Relation: Journal of Lie Theory Vol. 24, Issue 4, p. 957-967
Relation: http://www.heldermann.de/JLT/JLT24/JLT244/jlt24042.htm
Publisher: Heldermann Verlag
Resource Type: journal article
Date: 2014
Description: The Tits core G^ϯ of a totally disconnected locally compact group G is defined as the abstract subgroup generated by the closures of the contraction groups of all its elements. We show that a dense subgroup is normalised by the Tits core if and only if it contains it. It follows that every dense subnormal subgroup contains the Tits core. In particular, if G is topologically simple, then the Tits core is abstractly simple, and when G^ϯ is non-trivial, it is the smallest dense normal subgroup. The proofs are based on the fact, of independent interest, that the map which associates to an element the closure of its contraction group is continuous.
Subject: totally disconnected locally compact group; simple group; contraction group; Chabauty topology
Identifier: http://hdl.handle.net/1959.13/1304086
Identifier: uon:20792
Identifier: ISSN:0949-5932
Language: eng
Reviewed

		Thumbnail	File	Description	Size	Format