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# UnitLib

## The library of normalized unit groups of modular group algebras

Version 3.0.0

31 May 2009

Alexander Konovalov
Email: konovalov@member.ams.org
Homepage: http://www.cs.st-andrews.ac.uk/~alexk/
Address:
School of Computer Science
University of St Andrews
Jack Cole Building, North Haugh,
St Andrews, Fife, KY16 9SX, Scotland

Elena Yakimenko
Email: k-algebra@zsu.zp.ua
Address:
Department of Mathematics
Zaporozhye National University
Ul.Zhukovskogo, 66, Zaporozhye
69600 Ukraine

### Abstract

The UnitLib package extends the LAGUNA package and provides the library of normalized unit groups of modular group algebras of all finite p-groups of order not greater than 243 over the field of p elements.

It also contains a parallel implementation of the computation of the normalized unit group of a modular group algebra of a finite p-group (which should be retrieved from the GAP Small Groups Library) over the field of p elements.

### Copyright

© 2006-2009 by Alexander Konovalov and Elena Yakimenko

UnitLib 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. For details, see the FSF's own site http://www.gnu.org/licenses/gpl.html.

If you obtained UnitLib, we would be grateful for a short notification sent to one of the authors.

If you publish a result which was partially obtained with the usage of UnitLib, please cite it in the following form:

A. Konovalov and E. Yakimenko. UnitLib --- The library of normalized unit groups of modular group algebras, Version 3.0.0; 2009 (http://www.cs.st-andrews.ac.uk/~alexk/unitlib.htm).

### Acknowledgements

The first version of the package (as well as the subsequent version 2.1) was released in 2006, when the first author was a postdoctoral research collaborator at the Vrije Universiteit Brussels, Belgium. It is a pleasure of the first author to express his gratitude to Prof. Dr. Eric Jespers for his warm hospitality and to acknowledge the support provided by the Francqui Stichting grant ADSI107.

Both authors are very grateful to the members of the GAP team: Thomas Breuer, Stefan Kohl and Frank Lübeck for helpful suggestions. We would like to acknowledge Bettina Eick for communicating the package, and the referee for testing UnitLib and useful comments. Finally, we wish to thank the Centre for Interdisciplinary Research in Computational Algebra of the University of St Andrews and the Computational Cluster of the Kiev National Taras Shevchenko University for offering their computer facilities for computations.

### Contents

1 Introduction
1.1 General aims
1.2 Theoretical background
1.3 Installation and system requirements
2 UnitLib functions
2.1 MainFunctions
2.1-1 PcNormalizedUnitGroupSmallGroup
2.1-2 SavePcNormalizedUnitGroup
2.2 Service tools
2.2-1 UNITLIBBuildManual
2.2-2 UNITLIBBuildManualHTML
3 Details of implementation
3.1 Saving the data
3.2 Reading the data
4 An example of UnitLib usage
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