Orbit-blocking words in free groups

Abstract By strengthening known results about primitivity-blocking words in free groups, we prove that, for any 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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Publication Details

Journal
Journal of Group Theory
Published
2026-01-20
DOI
https://doi.org/10.1515/jgth-2025-0075
Primary Topic
Geometric and Algebraic Topology
Type
article
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article

Orbit-blocking words in free groups

Lucy Koch-Hyde, Eamonn Olive, Siobhán O’Connor
Journal of Group Theory
Geometric and Algebraic Topology
article

Orbit-blocking words in free groups

Lucy Koch-Hyde, Eamonn Olive, Siobhán O’Connor
article en

Abstract

Abstract By strengthening known results about primitivity-blocking words in free groups, we prove that, for any 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.

Journal of Group Theory
The Graduate Center, CUNY (US), City College of New York (US), New York Proton Center (US)
Reduced inequalities
Openalex Percentile: Top 76%
Geometric and Algebraic Topology
DOISourceOpenAlex
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