Narrow normal subgroups of Coxeter groups and of automorphism groups of Coxeter groups

Author:

Paris Luis1,Varghese Olga2

Affiliation:

1. IMB, UMR 5584, CNRS , Université Bourgogne , 21000 Dijon , France

2. Institute of Mathematics , Heinrich-Heine-University Düsseldorf , Universitätsstrasse 1, 40225 , Düsseldorf , Germany

Abstract

Abstract By definition, a group is called narrow if it does not contain a copy of a non-abelian free group. We describe the structure of finite and narrow normal subgroups in Coxeter groups and their automorphism groups.

Funder

Agence Nationale de la Recherche

Deutsche Forschungsgemeinschaft

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Reference26 articles.

1. G. Baumslag, Automorphism groups of residually finite groups, J. Lond. Math. Soc. 38 (1963), 117–118.

2. M. Bestvina, M. Feighn and M. Handel, The Tits alternative for Out ⁢ ( F n ) \mathrm{Out}(F_{n}) . I. Dynamics of exponentially-growing automorphisms, Ann. of Math. (2) 151 (2000), no. 2, 517–623.

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

4. N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Act. Sci. Indust. 1337, Hermann, Paris, 1968.

5. M. W. Davis, The Geometry and Topology of Coxeter Groups, London Math. Soc. Monogr. Ser. 32, Princeton University, Princeton, 2008.

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