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corefreesub

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

0.6

11 March 2024

Claudio Alexandre Piedade
Email: claudio.piedade@fc.up.pt
Homepage: https://www.fc.up.pt/pessoas/claudio.piedade/

Manuel Delgado
Email: mdelgado@fc.up.pt
Homepage: https://cmup.fc.up.pt/cmup/mdelgado/

Copyright

corefreesub package is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

Acknowledgements

The authors wish to thank all the comments, suggestions and issue reporting from users and developers of GAP, both past and future. Both authors were partially supported by CMUP, member of LASI, which is financed by Portuguese national funds through FCT – Fundação para a Ciência e a Tecnologia, I.P., under the project with references UIDB/00144/2020 and UIDP/00144/2020.

1 Introduction

1.1 Installation

1.2 Testing your installation

2 Obtaining Core-Free Subgroups

2.1 Core-Free Subgroups

  2.1-1 IsCoreFree
  2.1-2 CoreFreeConjugacyClassesSubgroups
  2.1-3 AllCoreFreeSubgroups

2.2 Degrees of Core-Free subgroups

2.2-1 CoreFreeDegrees

3 Faithful Transitive Permutation Representations

3.1 Obtaining Faithful Transitive Permutation Representations

3.1-1 FaithfulTransitivePermutationRepresentations

3.2 Faithful Transitive Permutation Representation of Minimal Degree