English

On an algorithm to decide whether a free group is a free factor of another

Group Theory 2008-08-01 v2

Abstract

We revisit the problem of deciding whether a finitely generated subgroup H is a free factor of a given free group F. Known algorithms solve this problem in time polynomial in the sum of the lengths of the generators of H and exponential in the rank of F. We show that the latter dependency can be made exponential in the rank difference rank(F) - rank(H), which often makes a significant change.

Keywords

Cite

@article{arxiv.math/0609552,
  title  = {On an algorithm to decide whether a free group is a free factor of another},
  author = {Pedro Silva and Pascal Weil},
  journal= {arXiv preprint arXiv:math/0609552},
  year   = {2008}
}

Comments

20 pages

R2 v1 2026-07-22T17:42:42.738Z