On quotients of Coxeter groups

2023/05/10 by Möller, Philip, Varghese, Olga · 3 citations
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2305.06207

Abstract

A group G is said to be just infinite if G itself is infinite but all proper quotients of G are finite. We show that a Coxeter group W_Γ is just infinite if and only if Γ is isomorphic to one of the following graphs: \widetildeA₁, \widetildeA_n (n≥ 2), \widetildeB_n (n≥ 3), \widetildeC_n (n≥ 2), \widetildeD_n(n≥ 4), \widetildeE₆, \widetildeE₇, \widetildeE₈, \widetildeF₄ or \widetildeG₂. Moreover, we show that just infinite Coxeter groups are profinitely rigid among all Coxeter groups.

Cited by

• On the derived length of Dyer groups
• Profinite rigidity of crystallographic groups arising from Lie theory
• Profinite properties of Coxeter groups

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