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# nq

## Nilpotent Quotients of Finitely Presented Groups

2.5.11

12 January 2024

Werner Nickel
Homepage: http://www.mathematik.tu-darmstadt.de/~nickel/

### Copyright

© 1992-2007 Werner Nickel

The nq package is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

### Acknowledgements

The author of ANU NQ is Werner Nickel.

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".

Since then, maintenance of ANU NQ has been taken over by Max Horn. All credit for creating ANU NQ still goes to Werner Nickel as sole author. However, bug reports and other inquiries should be sent to Max Horn.

The following are the original acknowledgements by Werner Nickel.

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.

Thanks to 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
5.1 Configuring for compilation
5.2 Compiling the nq binary
5.3 Testing
5.4 Feedback
A The nq command line interface
A.1 How to use the ANU NQ
A.2 The input format for presentations
A.3 An example
A.4 Some remarks about the algorithm
References
Index
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