Automorphic word maps and Amit--Ashurst conjecture

2023/09/16 by Harish Kishnani, Kishnani, Harish, Amit Kulshrestha +1
Computer Science · Mathematics · #20D15 #20F10 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2309.09010

openalex publication_date 2023/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• The Amit-Ashurst conjecture for finite metacyclic p-groups
• The Probability Distribution of Word Maps on Finite Groups
• On the probability of satisfying a word in nilpotent groups of class 2
• Word problems for finite nilpotent groups
• Word Images and Their Impostors in Finite Nilpotent Groups