Commensurations of the outer automorphism group of a universal Coxeter group

IF 0.6 3区数学 Q3 MATHEMATICS Groups Geometry and Dynamics Pub Date : 2021-01-18 DOI:10.4171/ggd/718

Yassine Guerch

引用次数: 1

Abstract

This paper studies the rigidity properties of the abstract commensurator of the outer automorphism group of a universal Coxeter group of rank $n$, which is the free product $W_n$ of $n$ copies of $\mathbb{Z}/2\mathbb{Z}$. We prove that for $n\geq 5$ the natural map $\mathrm{Out}(W_n) \to \mathrm{Comm}(\mathrm{Out}(W_n))$ is an isomorphism and that every isomorphism between finite index subgroups of $\mathrm{Out}(W_n)$ is given by a conjugation by an element of $\mathrm{Out}(W_n)$.

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一个泛Coxeter群的外自同构群的公度

本文研究了秩为$n$的泛Coxeter群的外自同构群的抽象共商的刚性性质，它是$\mathbb{Z}/2\mathbb｛Z}$的$n$个副本的自由积$W_n$。我们证明了对于$n\geq5$，自然映射$\mathrm｛Out｝（W_n）\ to \mathrm{Comm｝（\mathrm｝（W _n）。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Groups Geometry and Dynamics 数学-数学

CiteScore

1.10

自引率

0.00%

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审稿时长

>12 weeks

期刊介绍： Groups, Geometry, and Dynamics is devoted to publication of research articles that focus on groups or group actions as well as articles in other areas of mathematics in which groups or group actions are used as a main tool. The journal covers all topics of modern group theory with preference given to geometric, asymptotic and combinatorial group theory, dynamics of group actions, probabilistic and analytical methods, interaction with ergodic theory and operator algebras, and other related fields. Topics covered include: geometric group theory; asymptotic group theory; combinatorial group theory; probabilities on groups; computational aspects and complexity; harmonic and functional analysis on groups, free probability; ergodic theory of group actions; cohomology of groups and exotic cohomologies; groups and low-dimensional topology; group actions on trees, buildings, rooted trees.

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