The Amit-Ashurst conjecture for finite metacyclic p-groups

2022/01/13 by Rachel D. Camina, Camina, Rachel D., William M. Cocke +3
Computer Science · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2201.04860

openalex publication_date 2022/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Amit conjecture about word maps on finite nilpotent groups has been shown to hold for certain classes of groups. The generalised Amit conjecture says that the probability of an element occurring in the image of a word map on a finite nilpotent group G is either 0, or at least 1/|G|. Noting the work of Ashurst, we name the generalised Amit conjecture the Amit-Ashurst conjecture and show that the Amit-Ashurst conjecture holds for finite p-groups with a cyclic maximal subgroup.

Related

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