Computing the order and the index of a subgroup in a polycyclic group

TL;DR

This paper introduces a revised non-commutative Gauss algorithm for polycyclic groups, enabling the computation of subgroup order and index, which are crucial for understanding their algebraic structure.

Contribution

The paper presents an improved algorithm that efficiently determines the order and index of subgroups within polycyclic groups, advancing computational group theory methods.

Findings

Algorithm successfully computes subgroup order and index.

Enhances understanding of subgroup structure in polycyclic groups.

Potential applications in algebraic computations and group theory research.

Abstract

This contains a new version of the so-called non-commutative Gauss algorithm for polycyclic groups. Its results allow to read off the order and the index of a subgroup in an (possibly infinite) polycyclic group.