Library of normalized unit groups of modular group algebras

Version 4.0.0
Released 2018-05-01

This project is maintained by Alexander Konovalov

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GAP package UnitLib

Let KG be a group algebra of a finite p-group G over the field K of characteristic p, and let V(KG) be the normalized unit group of KG. The pc-presentation of the group V(KG) can be computed using the GAP package LAGUNA (https://gap-packages.github.io/laguna/), but for groups of orders 64 and more this computation already takes a lot of time.

The UnitLib package is an extension of the LAGUNA package that is aimed on this problem. It contains the library of normalized unit groups of modular group algebras of finite p-groups over the field of p elements. This allows the user to retrieve the pre-computed group from the library instead of the long-time computation. The group created with UnitLib will have the same properties and attributes as the one computed with LAGUNA.

The current version of UnitLib contains normalized unit groups V(KG) for all p-groups of order less than 243.

Libraries of normalized unit groups of groups of all orders not larger than 243, except for the order 128, are available in any operating system.

The library for groups of order 128 was compressed using gzip program and, therefore, will be available only in UNIX-type systems (including UNIX- installation in Mac OS X and Cygwin installation in Windows).

The UnitLib package is redistributed with GAP, but is not loaded by default. Therefore, to use UnitLib, first you need to load it as follows:

gap> LoadPackage("unitlib");

Alexander Konovalov and Elena Yakimenko