2021/10/22 by Dario Ascari, Ascari, Dario · 1 citation
Computer Science · Mathematics · #20E05 (20F65) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Topological and Geometric Data Analysis #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2110.11936
openalex publication_date 2021/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.