Achiral words

Achiral words

A word \(w\) in a free group is {\em achiral} if for every group \(G,\) \(G_w=G_{w^{-1}},\) where \(G_w\) is the image of the word map \(w\) on \(G.\) We will give few classes of examples of achiral words. Cocke and Ho asked whether Engel words are achiral or not. We will prove that it is enough to...

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Veröffentlicht in:arXiv.org 2023-02
Hauptverfasser: Singh, Shrinit, A Satyanarayana Reddy
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Mathematics - Combinatorics
Mathematics - Group Theory
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Zusammenfassung:A word \(w\) in a free group is {\em achiral} if for every group \(G,\) \(G_w=G_{w^{-1}},\) where \(G_w\) is the image of the word map \(w\) on \(G.\) We will give few classes of examples of achiral words. Cocke and Ho asked whether Engel words are achiral or not. We will prove that it is enough to apply Whitehead's algorithm to check the same.
ISSN:2331-8422
DOI:10.48550/arxiv.2302.02761