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arXiv · 2309.09010

Automorphic word maps and Amit--Ashurst conjecture

Harish Kishnani·Amit Kulshrestha
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Abstract

In this article, we address Amit--Ashurst conjecture on lower bounds of a probability distribution associated to a word on a finite nilpotent group. We obtain an extension of a result of Camina, Iniguez, and Thillaisundaram by providing improved bounds for the case of finite nilpotent groups of class $2$ for words in an arbitrary number of variables, and also settle the conjecture in some cases. We achieve this by obtaining words that are identically distributed on a group to a given word. In doing so, we also obtain an improvement of a result of Iniguez and Sangroniz using elementary techniques.

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Harish Kishnani, Amit Kulshrestha. 2023-09-16. Automorphic word maps and Amit--Ashurst conjecture. https://arxiv.org/abs/2309.09010

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