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# NQ

## A GAP 4 Package
computing nilpotent factor groups of finitely presented groups
Based on the ANU Nilpotent Quotient Program

Version 2.0

December 2002

Werner Nickel
e-mail: nickel@mathematik.tu-darmstadt.de
WWW: http://www.mathematik.tu-darmstadt.de/~nickel
Address:
Fachbereich Mathematik, AG 2
TU Darmstadt
Schlossgartenstr. 7
64289 Darmstadt
Germany

### Copyright

(C) 1992-2002 Werner Nickel.

### Acknowledgements

The development of this program was started while the author was supported by an Australian National University PhD scholarship and an Overseas Postgraduate Research Scholarship.

Further development of this program was done with support from the DFG-Schwerpunkt-Projekt "`Algorithmische Zahlentheorie und Algebra"'.

Over the years a number of people have made useful suggestions that found their way into the code: Mike Newman, Michael Vaughan-Lee, Joachim Neubüser, Charles Sims.

I thank Volkmar Felsch and Joachim Neubüser for their careful examination of the package prior to its release for GAP 4.

This documentation was prepared with the GAPDoc package by Frank Lübeck and Max Neunhöffer.

### Contents

1. Introduction
2. General remarks
2.1 Commutators and the Lower Central Series
2.2 Nilpotent groups
2.3 Nilpotent presentations
2.4 A sketch of the algorithm
2.5 Identical Relations
2.6 Expression Trees
2.7 A word about the implementation
2.8 The input format of the standalone
3. The Functions of the Package
3.1 Nilpotent Quotients of Finitely Presented Groups
3.1-1 NilpotentQuotient
3.1-2 NilpotentEngelQuotient
3.1-3 NqEpimorphismNilpotentQuotient
3.1-4 LowerCentralFactors
3.2 Expression Trees
3.2-1 ExpressionTrees
3.2-2 EvaluateExpTree
3.3 Auxiliary Functions
3.3-1 NqReadOutput
3.3-2 NqStringFpGroup
3.3-3 NqStringExpTrees
3.3-4 NqElementaryDivisors
3.4 Global Variables
3.4-1 NqRuntime
3.4-2 NqDefaultOptions
3.4-3 NqGlobalVariables
3.5 Diagnostic Output
4. Examples
4.1 Right Engel elements
5. Installation of the Package

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