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arXiv · 2110.11936

A fine property of Whitehead's algorithm

Dario Ascari
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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 $d$ for $d=1,2,3$, as well as $d=4$ in a special case.

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Dario Ascari. 2021-10-22. A fine property of Whitehead's algorithm. https://arxiv.org/abs/2110.11936

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