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# UnitLib

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

Version 2.0

August 2006

Alexander Konovalov
e-mail: konovalov@member.ams.org
WWW: http://homepages.vub.ac.be/~okonoval/
Address:
Department of Mathematics
Zaporozhye National University
Zaporozhye, 69063 Ukraine
Current address:
Department of Mathematics
Vrije Universiteit Brussel
Pleinlaan 2, Brussels
B-1050 Belgium

Elena Yakimenko
e-mail: 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.

### Copyright

(C) 2006 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 2.0; 2006 (http://homepages.vub.ac.be/~okonoval/unitlib.htm).

### Acknowledgements

We are very grateful to the members of the GAP team: Thomas Breuer, Stefan Kohl, Frank Lübeck for useful suggestions.

We acknowledge very much the Centre for Interdisciplinary Research in Computational Algebra of the University of St Andrews for possibility to use its computer facilities.

The main amount of computations was performed on the Computational Cluster of Kiev National Taras Shevchenko University, created with the support of Intel corporation (http://www.cluster.kiev.ua).

### Contents

1. Introduction
1.1 General aims
1.2 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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