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The LOOPS Package

Computing with quasigroups and loops in GAP

3.4.1

6 November 2018

Gábor Nagy
Email: nagyg@math.u-szeged.hu
Homepage: http://www.math.u-szeged.hu/~nagyg/
Address:
Bolyai Institute, University of Szeged
6725 Szeged, Aradi vertanuk tere 1
Hungary

Petr Vojtěchovský
Email: petr@math.du.edu
Homepage: http://www.math.du.edu/~petr/
Address:
Department of Mathematics, University of Denver
2280 S. Vine Street
Denver, CO 80208
USA

Abstract

The LOOPS package provides researchers in nonassociative algebra with a computational tool that integrates standard notions of loop theory with libraries of loops and group-theoretical algorithms of GAP. The package also expands GAP toward nonassociative structures.

Copyright

© 2005-2017 Gábor P. Nagy and Petr Vojtěchovský.

The LOOPS 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

We thank the following people for sending us remarks and comments, and for suggesting new functionality of the package: Muniru Asiru, Bjoern Assmann, Andreas Distler, Aleš Drápal, Graham Ellis, Steve Flammia, Kenneth W. Johnson, Michael K. Kinyon, Alexander Konovalov, Frank Lübeck, Jonathan D.H. Smith, David Stanovský and Glen Whitney.

The library of Moufang loops of order 243 was generated from data provided by Michael C. Slattery and Ashley L. Zenisek. The library of right conjugacy closed loops of order less than 28 was generated from data provided by Katharina Artic. The library of right Bruck loops of order 27, 81 was obtained jointly with Izabella Stuhl.

Gábor P. Nagy was supported by OTKA grants F042959 and T043758, and Petr Vojtěchovský was supported by the 2006 and 2016 University of Denver PROF grants and the Simons Foundation Collaboration Grant 210176.

Contents

1 Introduction
2 Mathematical Background
3 How the Package Works
4 Creating Quasigroups and Loops
5 Basic Methods And Attributes
6 Methods Based on Permutation Groups
7 Testing Properties of Quasigroups and Loops
8 Specific Methods
9 Libraries of Loops
A Files
B Filters
References
Index

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