Vladimir Shpilrain
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Automorphic orbits in free groups: recent progress
gcc:16639 -
journal of Groups, complexity, cryptology,
June 19, 2026,
Volume 18, Issue 1, Special issue in honour of Alexei Miasnikov
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https://doi.org/10.46298/jgcc.2026.18.1.16639Automorphic orbits in free groups: recent progressArticle
Authors: Vladimir Shpilrain
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Vladimir Shpilrain
In this survey, we describe recent progress on asymptotic properties of various automorphic orbits in free groups. In particular, we address the problem of counting potentially positive elements of a given length. We also discuss complexity (worst-case, average-case, and generic-case) of Whitehead's automorphism problem and relevant properties of automorphic orbits, including orbit-blocking words.
8 pages. Published in the journal of Groups, Complexity, Cryptology
Volume: Volume 18, Issue 1, Special issue in honour of Alexei Miasnikov
Published on: June 19, 2026
Accepted on: June 15, 2026
Submitted on: October 5, 2025
Keywords: Group Theory