On the coherence of one-relator groups and their group algebras

• 成果类型: Article
• 署名作者: Jaikin-Zapirain, Andrei; Linton, Marco
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2025.201.3.4
• 发表日期: 2025
• 页码: 909-959
• 关键词: division rings; SUBGROUPS; fractions; PRODUCTS; conjecture; ELEMENTS; torsion; THEOREM

摘要

We prove that one-relator groups are coherent, solving a well-known problem of Gilbert Baumslag. Our proof strategy is readily applicable to many classes of groups of cohomological dimension two. We show that fundamental groups of two complexes with non-positive immersions are homologically coherent, we show that groups with staggered presentations and many Coxeter groups are coherent and we show that group algebras over fields of characteristic zero of groups with reducible presentations without proper powers are coherent.