GAP Package HeLP

HeLP is a package to compute constraints on partial augmentations of torsion units in integral group rings using a method developed by Luthar, Passi and Hertweck. The package can be employed to verify the Zassenhaus Conjecture, the Prime Graph Question, the Spectrum Problem and the Kimmerle Problem for finite groups, once characters are known. It uses an interface to the software package 4ti2 to solve integral linear inequalities or alternatively Normaliz.

The current version of this package is version 4.1, released on 2026-01-09. For more information, please refer to the package manual. There is also a README file.

License: GPL-2.0-or-later

Dependencies

This package requires GAP version >=4.13

The following other GAP packages are needed:

io >=4.2
CTblLib >= 1.2.2

The following additional GAP packages are not required, but suggested:

4ti2Interface >= 2015.04.29
NormalizInterface >= 1.4.1

Authors

Andreas Bächle, Leo Margolis.

Citing

Please, cite this package as

[BM26] Bächle, A. and Margolis, L., HeLP, Hertweck-Luthar-Passi method., Version 4.1 (2026)
(GAP package), https://gap-packages.github.io/HeLP.

You can get more info by typing Cite("HeLP"); in the gap prompt.

Feedback

For bug reports, feature requests and suggestions, please use the issue tracker.