English

Virtual First Betti Number of GGS Groups

Group Theory 2025-05-30 v1

Abstract

We observe a criterion for groups to have vanishing virtual first Betti number and use it to give infinitely many examples of torsion-free, finitely generated, residually finite groups which aren't virtually diffuse. This answers a question raised by Kionke and Raimbault.

Keywords

Cite

@article{arxiv.2505.23269,
  title  = {Virtual First Betti Number of GGS Groups},
  author = {Andrew Ng},
  journal= {arXiv preprint arXiv:2505.23269},
  year   = {2025}
}