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Random groups and nonarchimedean lattices

Part of: Special aspects of infinite or finite groups Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  16 October 2014

SYLVAIN BARRÉ  and
MIKAËL PICHOT
SYLVAIN BARRÉ
Affiliation:
Université de Bretagne Sud, Université Européenne de Bretagne, France; [email protected]
MIKAËL PICHOT
Affiliation:
Department of Mathematics & Statistics, McGill University, Montréal, Québec,Canada H3A 2K6; [email protected]

Abstract

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We consider models of random groups in which the typical group is of intermediate rank (in particular, it is not hyperbolic). These models are parallel to Gromov’s well-known constructions, and include for example a ‘density model’ for groups of intermediate rank. The main novelty is the higher rank nature of the random groups. They are randomizations of certain families of lattices in algebraic groups (of rank 2) over local fields.

MSC classification

Secondary: 20F65: Geometric group theory 20E42: Groups with a $BN$-pair; buildings 20E18: Limits, profinite groups
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 2 , 01 July 2014 , e26
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/3.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2014

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