Isomorphism and non-isomorphism for interval groups of type D_n

2022/06/27 by Barbara Baumeister, Baumeister, Barbara, Derek F. Holt +5
Computer Science · Mathematics · #20-08 #20F36 #20F55 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2206.13308

openalex publication_date 2022/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider presentations that were derived in \citeBaumeisterNeaimeRees for the interval groups associated with proper quasi-Coxeter elements of the Coxeter group W(D_n). We use combinatorial methods to derive alternative presentations for the groups, and use these new presentations to show that the interval group associated with a proper quasi-Coxeter element of W(D_n) cannot be isomorphic to the Artin group of type D_n. While the specific problems we solve arise from the study of interval groups, their solution provides an illustration of how techniques indicated by computational observation can be used to derive properties of all groups within an infinite family.

Related

• Interval groups related to finite Coxeter groups I
• Interval groups related to finite Coxeter groups, Part II
• The dual Artin isomorphism for Artin groups of XXL type
• A family of non-isomorphism results
• The isomorphism problem for Coxeter groups