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arXiv · 2505.00477

Orbit-blocking words in free groups

Lucy Koch-Hyde·Siobhan O'Connor·Eamonn Olive·Vladimir Shpilrain
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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.

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Lucy Koch-Hyde, Siobhan O'Connor, Eamonn Olive, Vladimir Shpilrain. 2025-05-01. Orbit-blocking words in free groups. https://arxiv.org/abs/2505.00477

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