English

A characterisation of virtually free groups

Group Theory 2011-11-04 v1

Abstract

We prove that a finitely generated group GG is virtually free if and only if there exists a generating set for GG and k>0k > 0 such that all kk-locally geodesic words with respect to that generating set are geodesic.

Keywords

Cite

@article{arxiv.1111.0771,
  title  = {A characterisation of virtually free groups},
  author = {Robert H. Gilman and S. Hermiller and Derek F. Holt and Sarah Rees},
  journal= {arXiv preprint arXiv:1111.0771},
  year   = {2011}
}
R2 v1 2026-06-21T19:30:17.491Z