On the coherence of one-relator groups and their group algebras
Group Theory
2025-02-05 v4
Abstract
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.
Keywords
Cite
@article{arxiv.2303.05976,
title = {On the coherence of one-relator groups and their group algebras},
author = {Andrei Jaikin-Zapirain and Marco Linton},
journal= {arXiv preprint arXiv:2303.05976},
year = {2025}
}
Comments
40 pages. Version accepted for publication at the Annals of Mathematics