English

The Amit-Ashurst conjecture for finite metacyclic p-groups

Group Theory 2023-05-09 v3

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.

Keywords

Cite

@article{arxiv.2201.04860,
  title  = {The Amit-Ashurst conjecture for finite metacyclic p-groups},
  author = {Rachel D. Camina and William Cocke and Anitha Thillaisundaram},
  journal= {arXiv preprint arXiv:2201.04860},
  year   = {2023}
}

Comments

10 pages, revised version

R2 v1 2026-06-24T08:48:39.776Z