Orbit-blocking words in free groups
Group Theory
2025-08-11 v2 Computational Complexity
Abstract
By strengthening known results about primitivity-blocking words in free groups, we prove that for any nontrivial element w of a free group of finite rank, there are words that cannot be subwords of any cyclically reduced automorphic image of w. This has implications for the average-case complexity of a variant of Whitehead's problem.
Cite
@article{arxiv.2505.00477,
title = {Orbit-blocking words in free groups},
author = {Lucy Koch-Hyde and Siobhan O'Connor and Eamonn Olive and Vladimir Shpilrain},
journal= {arXiv preprint arXiv:2505.00477},
year = {2025}
}
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11 pages