Geodesic
A fine property of Whitehead's algorithm
Dario Ascari1 orcid
1University of Oxford, UK
Groups, geometry, and dynamics, Tome 18 (2024) no. 1, pp. 235-264

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DOI

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. These refinements allow us to prove new results about primitive elements and free factors in a free group, including 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.
DOI : 10.4171/ggd/746
Classification : 20-XX
Mots-clés : Free groups, Whitehead's algorithm, free factor

Dario Ascari  1

1 University of Oxford, UK 
Dario Ascari. A fine property of Whitehead's algorithm. Groups, geometry, and dynamics, Tome 18 (2024) no. 1, pp. 235-264. doi: 10.4171/ggd/746
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