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arXiv · 2302.02761

Achiral words

Shrinit Singh·A. Satyanarayana Reddy
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Abstract

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.

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Shrinit Singh, A. Satyanarayana Reddy. 2023-02-02. Achiral words. https://doi.org/10.1080/00927872.2024.2377805

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