Orbit-blocking words in free groups

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.

Publication Details

Journal
ArXiv.org
Published
2025-05-01
Primary Topic
Geometric and Algebraic Topology
Type
article
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article

Orbit-blocking words in free groups

ArXiv.org
Geometric and Algebraic Topology
article

Orbit-blocking words in free groups

article en

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.

ArXiv.org
Reduced inequalities
Openalex Percentile: Top 45%
Geometric and Algebraic Topology
Open Access PDFOpenAlex
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Orbit-blocking words in free groups · ArXiv.org (2025) | TGRS Research Map | TGRS