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Mathematics > Group Theory

Title: Achiral words

Authors: Shrinit Singh, A. Satyanarayana Reddy
(Submitted on 2 Feb 2023)
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.
Comments: 7 pages
Subjects: Group Theory (math.GR); Combinatorics (math.CO)
MSC classes: 20F10
Cite as: arXiv:2302.02761 [math.GR]
  (or arXiv:2302.02761v1 [math.GR] for this version)

Submission history

From: Arikatla Satyanarayana Reddy [view email]
[v1] Thu, 2 Feb 2023 17:46:24 GMT (8kb)
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