English

Coherence for elementary amenable groups

Group Theory 2025-01-15 v2 Rings and Algebras

Abstract

We prove that for an elementary amenable group, coherence of the group, homological coherence of the group, and coherence of the integral group ring are all equivalent. This generalises a result of Bieri and Strebel for finitely generated soluble groups.

Keywords

Cite

@article{arxiv.2302.03346,
  title  = {Coherence for elementary amenable groups},
  author = {Sam Hughes and Dawid Kielak and Peter H. Kropholler and Ian J. Leary},
  journal= {arXiv preprint arXiv:2302.03346},
  year   = {2025}
}

Comments

v2. updated with referee's comments, to appear in Proceedings of the American Mathematical Society; v1. 10 pages, comments welcome!