## &LAGUNA;

Lie AlGebras and UNits of group Algebras
Version 3.3.1
Victor Bovdi vbovdi@math.klte.hu

               Institute of Mathematics and Informatics

    	   University of Debrecen

    	   P.O.Box 12, Debrecen, H-4010 Hungary

Alexander Konovalov konovalov@member.ams.org http://ukrgap.exponenta.ru/konoval.htm

                Department of Mathematics

        	    Zaporozhye State University

                P.O.Box 1317, Central Post Office

                Zaporozhye, 69000 Ukraine

Richard Rossmanith richard.rossmanith@d-fine.de

        	    d-fine GmbH

                Mergenthalerallee 55
                65760 Eschborn/Frankfurt

                Germany

Csaba Schneider csaba.schneider@sztaki.hu http://www.sztaki.hu/~schneider

                Informatics Laboratory

                Computer and Automation Research Institute

                The Hungarian Academy of Sciences

    	    1111 Budapest, Lagymanyosi u. 11, Hungary

May 2005

&LAGUNA; package The title ``&LAGUNA;'' stands for ``Lie AlGebras and UNits of group Algebras''. This is the new name of the &GAP;4 package &LAG;, which is thus replaced by &LAGUNA;.

&LAGUNA; extends the &GAP; functionality for computations in group rings. Besides computing some general properties and attributes of group rings and their elements, &LAGUNA; is able to perform two main kinds of computations. Namely, it can verify whether a group algebra of a finite group satisfies certain Lie properties; and it can calculate the structure of the normalized unit group of a group algebra of a finite p-group over the field of p elements.

&copyright; 2003 by Victor Bovdi, Alexander Konovalov, Richard Rossmanith, and Csaba Schneider

We adopt the copyright regulations of &GAP; from the copyright notice in the &GAP; manual.

If you obtained &LAGUNA;, 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 &LAGUNA;, please cite it in the following form:

V. Bovdi, A. Konovalov, R. Rossmanith and C. Schneider. LAGUNA --- Lie AlGebras and UNits of group Algebras, Version 3.3.1; 2005 (http://ukrgap.exponenta.ru/laguna.htm).

Some of the features of &LAGUNA; were already included in the &GAP;4 package &LAG; written by the third author, Richard Rossmanith. The three other authors first would like to thank Greg Gamble for maintaining &LAG; and for upgrading it from version 2.0 to version 2.1, and Richard Rossmanith for allowing them to update and extend the &LAG; package. We are also grateful to Wolfgang Kimmerle for organizing the workshop ``Computational Group and Group Ring Theory'' (University of Stuttgart, 28--29 November, 2002), which allowed us to meet and have fruitful discussions that led towards the final &LAGUNA; release.

We are all very grateful to the members of the &GAP; team: Thomas Breuer, Willem de Graaf, Alexander Hulpke, Stefan Kohl, Steve Linton, Frank Lübeck, Max Neunhöffer and many other colleagues for helpful comments and advise. We acknowledge very much Herbert Pahlings for communicating the package and the referee for careful testing &LAGUNA; and useful suggestions.

A part of the work on upgrading &LAG; to &LAGUNA; was done in 2002 during Alexander Konovalov's visits to Debrecen, St Andrews and Stuttgart Universities. He would like to express his gratitude to Adalbert Bovdi and Victor Bovdi, Colin Campbell, Edmund Robertson and Steve Linton, Wolfgang Kimmerle, Martin Hertweck and Stefan Kohl for their warm hospitality, and to the NATO Science Fellowship Program, to the London Mathematical Society and to the DAAD for the support of these visits.

<#Include SYSTEM "intro.xml"> <#Include SYSTEM "example.xml"> <#Include SYSTEM "theory.xml"> <#Include SYSTEM "funct.xml">