Hall polynomials for the torsion free groups of Hirsch length at most 5

TL;DR

This paper explicitly constructs Hall polynomials for torsion free nilpotent groups with Hirsch length up to 5, enabling algebraic computations in these groups.

Contribution

It provides explicit Hall polynomials for all torsion free nilpotent groups of Hirsch length at most 5, extending the practical computational tools available.

Findings

Explicit Hall polynomials for groups of Hirsch length 3, 4, and 5

Facilitates algebraic computations in these groups

Extends previous theoretical results to concrete formulas

Abstract

A theorem by Hall asserts that the multiplication in torsion free nilpotent groups of finite Hirsch length can be facilitated by polynomials. In this note we exhibit explicit Hall polynomials for the torsion free nilpotent groups of Hirsch length at most 5.