LOOPS: Computing with quasigroups and loops in GAP

Gábor P. Nagy (University of Szeged, Hungary)
Petr Vojtěchovský (University of Denver, USA)

This is the official distribution webpage of the LOOPS package for GAP 4. You will find here:

Note: The package has been submitted to GAP on October 15, 2004 and is now available with the standard distribution of GAP. It continues to evolve according to the comments of the referees and users.

Brief description

LOOPS is a package for GAP 4 whose purpose is to provide researchers in nonassociative algebra with a powerful computational tool concerning finite loops and quasigroups; and to extend GAP toward the realm of nonassociative structures.

The package consists of three complementary parts: core methods for quasigroups and loops, specific methods for loops (mainly Moufang loops), libraries of small loops.

Installation instructions

To install LOOPS, you must have GAP version 4.4 installed on your computer. Then

  1. download any of the available versions (Windows, Unix) of LOOPS
  2. unpack the file into the pkg directory of GAP

After this step, you will see the subfolder loops in the pkg folder.

To load LOOPS into GAP, start GAP and use LoadPackage( "loops" );.

If you prefer LOOPS to load automatically anytime you start GAP, edit the value of Autoload in the file loops/PackageInfo.g from false to true.


The most recent version of LOOPS is 2.2.0.

Before you download LOOPS, you might want to check the README.loops and PackageInfo.g files, and the documentation.


The documentation for the package is included with the distribution and is located in the loops/doc folder. You can also access the documentation directly from here.

New features

In version 2.2.0:

In version 2.1.3:

In version 2.1.2:

In version 2.1.1:

In version 2.1.0:

Click to see the log of older changes.

Known bugs in the most recent version

IsotopismLoops correctly decides if two loops are isotopic but when they are, it does not return a correct isotopism.

Older versions of the package

Since several published papers rely on older versions of the package, we post them here so that calculations can be verified.

For Unix: version 1.0.0, 1.1.0, 1.2.0, 1.3.0, 1.4.0, 1.5.0, 1.9.0, 2.0.0, 2.1.0, 2.1.1, 2.1.2, 2.1.3.

For Windows: version 1.0.0, 1.1.0, 1.2.0, 1.3.0, 1.4.0, 1.5.0, 1.9.0, 2.0.0, 2.1.0, 2.1.1, 2.1.2, 2.1.3.


While developing the LOOPS package, G. P. Nagy was supported by the OTKA grants F042959 and T043758.

While working toward LOOPS version 2.0.0, Petr Vojtechovsky was supported by the 2006 PROF grant of the University of Denver.

We thank Muniru Asiru, Bjoern Assmann, Andreas Distler, Steve Flammia, Kenneth W. Johnson, Michael K. Kinyon, Alexander Konovalov, Frank Luebeck, Muhammad Shah and Jonathan D. H. Smith for comments and suggestions.

last update: July 2, 2012