# HeLP

Hertweck-Luthar-Passi method.

Version 3.4
Released 2018-11-20

This project is maintained by Andreas Bächle, Leo Margolis

# 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 and the Prime Graph Question for finite groups, once characters are known. It uses an interface to the software package 4ti2 to solve integral linear inequalities.

The current version of this package is version 3.4, released on 2018-11-20. For more information, please refer to the package manual. There is also a README file.

A short article outlining the theory and algorithms is available here or in the ArXiv version.

## Installation

Download and unpack the archive provided below in the pkg subdirectory of your GAP installation. This completes the installation of the HeLP package. Note however that this package requires the 4ti2Interface, which in turn uses the package IO. The latter package needs a C-part to be compiled; see the readme-file or the documentation of that package. The HeLP-package also requires the GAP-package NormalizInterface which also has to be build before it can be loaded in GAP; see the readme-file or the documentation of that package. This package also makes use of the software Normaliz and, if installed, 4ti2 and lrslib. The first one should automatically be installed when building the NormalizInterface, the second and the third one need to be installed manually as described homepages of the packages. In case you have problems getting the HeLP-package running, see Section 6.1 of the manual for some trouble shooting. If this does not help, feel free to contact one of the maintainers of the package.

## Dependencies

This package requires GAP version >=4.8.2

The following other GAP packages are needed:

## Citing

[BM18] Bächle, A. and Margolis, L., HeLP, Hertweck-Luthar-Passi method., Version 3.4 (2018)
(GAP package), https://gap-packages.github.io/HeLP.

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

We would be grateful to hear if you are using this package. Just send an email to one of the maintainers. Comments and suggestion for improvements are very welcome.

## Acknowledgments

The development of HeLP was partially supported by the DFG priority program SPP 1489 Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory and the Research Foundation Flanders (FWO - Vlaanderen).

## Feedback

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