paper

Orbit-blocking words in free groups

arXiv:2505.00477

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.

11 pages

Orbit-blocking words in free groups · wovepaper