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1 October 2013 Trees, contraction groups, and Moufang sets
Pierre-Emmanuel Caprace, Tom De Medts
Duke Math. J. 162(13): 2413-2449 (1 October 2013). DOI: 10.1215/00127094-2371640

Abstract

We study closed subgroups G of the automorphism group of a locally finite tree T acting doubly transitively on the boundary. We show that if the stabilizer of some end is metabelian, then there is a local field k such that PSL2(k)GPGL2(k). We also show that the contraction group of some hyperbolic element is closed and torsion-free if and only if G is (virtually) a rank 1 simple p-adic analytic group for some prime p. A key point is that if some contraction group is closed, then G is boundary-Moufang, meaning that the boundary T is a Moufang set. We collect basic results on Moufang sets arising at infinity of locally finite trees, and we provide a complete classification in case the root groups are torsion-free.

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Pierre-Emmanuel Caprace. Tom De Medts. "Trees, contraction groups, and Moufang sets." Duke Math. J. 162 (13) 2413 - 2449, 1 October 2013. https://doi.org/10.1215/00127094-2371640

Information

Published: 1 October 2013
First available in Project Euclid: 8 October 2013

zbMATH: 1291.20025
MathSciNet: MR3127805
Digital Object Identifier: 10.1215/00127094-2371640

Subjects:
Primary: 20E08
Secondary: 20E42 , 20G25 , 22D05

Rights: Copyright © 2013 Duke University Press

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Vol.162 • No. 13 • 1 October 2013
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