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Automorphismes du groupe des automorphismes d’un groupe de Coxeter universel

Yassine Guerch

Algebraic & Geometric Topology 24 (2024) 251–276
Abstract

À l’aide de l’outre-espace de Guirardel et Levitt d’un produit libre, nous démontrons que le groupe des automorphismes extérieurs du groupe des automorphismes extérieurs du groupe de Coxeter universel de rang n 5 est trivial, et qu’il s’agit d’un groupe cyclique d’ordre 2 si n = 4. Nous démontrons aussi que le groupe des automorphismes extérieurs du groupe des automorphismes du groupe de Coxeter universel de rang n 4 est trivial.

Using the Guirardel–Levitt outer space of a free product, we prove that the outer automorphism group of the outer automorphism group of the universal Coxeter group of rank n 5 is trivial, and that it is a cyclic group of order 2 if n = 4. In addition we prove that the outer automorphism group of the automorphism group of the universal Coxeter group of rank n 4 is trivial.

Keywords
universal Coxeter group, outer automorphism groups, outer space, graph of groups
Mathematical Subject Classification
Primary: 20E08, 20E36, 20F28, 20F55
References
Publication
Received: 10 May 2021
Accepted: 23 October 2022
Published: 18 March 2024
Authors
Yassine Guerch
Laboratoire de mathématique d’Orsay
Université Paris-Saclay
UMR 8628 CNRS
Orsay
France
ENS-Lyon
UMR 5669 CNRS
Université de Lyon, UMPA
Lyon
France

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