Tits alternative for Artin groups of type FC

Author:

Martin Alexandre1,Przytycki Piotr2

Affiliation:

1. Department of Mathematics and the Maxwell Institute for Mathematical Sciences , Heriot-Watt University , Riccarton , Edinburgh EH14 4AS , United Kingdom

2. Department of Mathematics and Statistics , McGill University , Burnside Hall, 805 Sherbrooke Street West , Montreal , QC, H3A 0B9 , Canada

Abstract

Abstract Given a group action on a finite-dimensional CAT ( 0 ) {\mathrm{CAT}(0)} cube complex, we give a simple criterion phrased purely in terms of cube stabilisers that ensures that the group satisfies the strong Tits alternative, provided that each vertex stabiliser satisfies the strong Tits alternative. We use it to prove that all Artin groups of type FC satisfy the strong Tits alternative.

Funder

Engineering and Physical Sciences Research Council

Natural Sciences and Engineering Research Council of Canada

Simons Foundation

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Reference29 articles.

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3. M. Bestvina, M. Feighn and M. Handel, The Tits alternative for Out ⁢ ( F n ) {{\rm Out}(F_{n})} . II. A Kolchin type theorem, Ann. of Math. (2) 161 (2005), no. 1, 1–59.

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1. The Tits alternative for two-dimensional Artin groups and Wise's power alternative;Journal of Algebra;2023-08

2. Groups acting on CAT(0) cube complexes with uniform exponential growth;Algebraic & Geometric Topology;2023-03-27

3. Parabolic subgroups of large-type Artin groups;Mathematical Proceedings of the Cambridge Philosophical Society;2022-09-12

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