Enumerating fibres of commutator words over p-groups

TL;DR

This paper investigates the structure of fibers of commutator word maps over specific p-groups, providing enumeration results and examples for groups of certain classes and exponents.

Contribution

It introduces a detailed enumeration of fibers of commutator word maps over p-groups with nilpotency class less than p and exponent p, including all word maps over class 2 groups.

Findings

Enumerated fibers of commutator word maps over p-groups of nilpotency class less than p

Provided examples and enumerations for all word maps over p-groups of class 2 with exponent p

Enhanced understanding of the structure of word maps in specific p-group classes

Abstract

We enumerate the fibres of commutator word maps over p-groups of nilpotency class less than p with exponent p. We also give some examples and enumerate the fibre sizes of all word maps over p-groups of class 2 with exponent p.