English

Elliptic subgroups in cyclic splittings of a free group

Group Theory 2023-11-06 v1

Abstract

We use Gersten's generalization of Whitehead's algorithm to determine whether a given finitely generated subgroup of a free group FF is elliptic in an elementary cyclic splitting of FF. We provide a similar result for all elementary cyclic splittings of a free group of rank two and partial results towards an algorithm for ellipticity in elementary cyclic splittings of FF as an HNN-extension.

Keywords

Cite

@article{arxiv.2311.01668,
  title  = {Elliptic subgroups in cyclic splittings of a free group},
  author = {Brent B. Solie},
  journal= {arXiv preprint arXiv:2311.01668},
  year   = {2023}
}

Comments

24 pages, 7 figures