## &UnitLib;

The library of normalized unit groups of modular group algebras
Version 3.0.0
Alexander Konovalov konovalov@member.ams.org http://www.cs.st-andrews.ac.uk/˜alexk/

                School of Computer Science

                University of St Andrews

                Jack Cole Building, North Haugh,

                St Andrews, Fife, KY16 9SX, Scotland

Elena Yakimenko k-algebra@zsu.zp.ua

                Department of Mathematics

                Zaporozhye National University

                Ul.Zhukovskogo, 66, Zaporozhye

    	        69600 Ukraine

31 May 2009

&UnitLib; package

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).
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.
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