May 27, 2024Open Access

Word maps, polynomial maps and image ratios

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Abstract

If A is a finite group (or a finite ring) and is a word map (or a polynomial map), we define the quantity | (A) |/|A| as the image ratio of on A and will be denoted by (, A). In this article, we investigate the set R () =\ (, A): A is a finite group\, and also consider the case of rings. Specifically, we demonstrate the existence of word maps (and polynomial maps) whose set of image ratios is dense in 0, 1 for both groups (and rings).

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Saikat Panja (Mon,) studied this question.

synapsesocial.com/papers/68e68593b6db64358760dec2 https://doi.org/https://doi.org/10.48550/arxiv.2405.17026

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