GAP package LAGUNA

The title “LAGUNA” stands for “Lie AlGebras and UNits of group Algebras”.

LAGUNA extends 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.

LAGUNA does not use external binaries and, therefore, works without restrictions on the type of the operating system. It is redistributed with and is loaded by default. If it is not loaded due to the specific user settings, load it using the following command:

gap> LoadPackage("laguna");

History and Acknowledgements

Some of the features of LAGUNA were already included in the GAP4 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 the organisation of the workshop “Computational Group and Group Rings Theory” (University of Stuttgart, 28-29 November, 2002) which allowed us to meet together 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 Luebeck, Max Neunhoeffer and many other colleagues for hepful 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 Olexandr 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 Programme, to the London Mathematical Society and to the DAAD for the support of this visits.

See the file ChangeLog for the details about changes introduced in each LAGUNA release.

Victor Bovdi, Olexandr Konovalov, Richard Rossmanith and Csaba Schneider