Decomposability of Finitely Generated Torsion-free Nilpotent Groups

TL;DR

This paper presents an algorithm to determine whether finitely generated torsion-free nilpotent groups can be decomposed into direct products of smaller subgroups, aiding structural analysis of such groups.

Contribution

It introduces a novel algorithm for deciding decomposability of finitely generated torsion-free nilpotent groups, advancing computational group theory.

Findings

Algorithm successfully determines decomposability

Provides a practical tool for structural analysis

Enhances understanding of nilpotent group decomposition

Abstract

We describe an algorithm for deciding whether or not a given finitely generated torsion-free nilpotent group is decomposable as the direct product of nontrivial subgroups.