fingolfin / corefreesub

A GAP Package for the calculation of core-free subgroups and their faithful transitive permutation representations

GAP Package corefreesub

The CoreFreeSub package is a package to compute faithful transitive permutation representations (FTPRs) of groups. Moreover, this package provides tools to determine the degrees of these FTPRs and lists core-free subgroups. Furthermore, this package allows a graph representation of the permutation representations.

The current version of this package is version 0.3. For more information, please refer to the package manual, in the "doc" folder.

Dependencies

This package requires GAP version at least 4.11.

Authors

Claudio Alexandre Piedade & Manuel Delgado

Citing

Please, cite this package as

[PD23] Piedade, C. A. and Delgado, M., corefreesub, A GAP Package for calculating the core-free subgroups and their faithful transitive permutation representations, Version 0.3 (2023), GAP package, https://CAPiedade.github.io/corefreesub/.

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

Features

The features of this package include

• function to check whether a subgroup is core-free;
• computing (conjugacy classes of) subgroups which are core-free;
• computing faithful transitive permutation representations (FTPRs) and respective degrees;
• computing minimal FTPRs and respective minimal degree;
• DOT file construction of the FTPRs
• Visualization of the DOT file and TeX file output.

There is a manual in the sub-directory doc written using the GAP package gapdoc which describes the available functions in detail. The pdf, html versions of the manual are also available there.

Contact and Feedback

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

License

This package is under GPL 2.0 license or later.