Coxeter quotients of the automorphism group of a Coxeter group

Olga Varghese

Coxeter quotients of the automorphism group of a Coxeter group

Group Theory 2022-09-05 v3

Authors: Olga Varghese

Abstract

We show that for a large class $\mathcal{W}$ of Coxeter groups the following holds: Given a group $W_\Gamma$ in $\mathcal{W}$ , the automorphism group ${\rm Aut}(W_\Gamma)$ virtually surjects onto some infinite Coxeter group. In particular, the group ${\rm Aut}(W_\Gamma)$ is virtually indicable and therefore does not have Kazhdan's property (T).

Keywords

coxeter groups automorphism groups coxeter quotients virtual surjection kazhdan property (t) indicable groups

Cite

@article{arxiv.2003.04111,
  title  = {Coxeter quotients of the automorphism group of a Coxeter group},
  author = {Olga Varghese},
  journal= {arXiv preprint arXiv:2003.04111},
  year   = {2022}
}

Comments

Completely rewritten because the proof of Theorem A in the previous version is incomplete

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