A nilpotent quotient algorithm for L-presented groups

TL;DR

This paper presents a nilpotent quotient algorithm tailored for L-presented groups, details its implementation in GAP, and introduces new infinite series of L-presented groups as applications and examples.

Contribution

It introduces a novel nilpotent quotient algorithm for L-presented groups and demonstrates its practical implementation and applications within GAP.

Findings

Successful implementation of the algorithm in GAP

Introduction of two new infinite series of L-presented groups

Demonstrated applications of the algorithm with these groups

Abstract

The main part of this paper contains a description of a nilpotent quotient algorithm for L-presented groups and a report on applications of its implementation in the computer algebra system GAP. The appendix introduces two new infinite series of L-presented groups. Apart from being of interest in their own right, these new L-presented groups serve as examples for applications of the nilpotent quotient algorithm.