A fine property of Whitehead's algorithm
Group Theory
2021-10-25 v1
Abstract
We develop a refinement of Whitehead's algorithm for primitive words in a free group. We generalize to subgroups, establishing a strengthened version of Whitehead's algorithm for free factors. We make use of these refinements in proving new results about primitive elements and free factors in a free group. These include a relative version of Whitehead's algorithm, and a criterion that tests whether a subgroup is a free factor just by looking at its primitive elements. We develop an algorithm to determine whether or not two vertices in the free factor complex have distance for , as well as in a special case.
Cite
@article{arxiv.2110.11936,
title = {A fine property of Whitehead's algorithm},
author = {Dario Ascari},
journal= {arXiv preprint arXiv:2110.11936},
year = {2021}
}
Comments
21 pages, 6 figures