low-index

Low Index Subgroups

The low_index project provides a Python module which implements a variant of Charles Sims' Low Index Subgroups algorithm for enumerating all of the conjugacy classes of subgroups of a finitely presented group with finite index less than a given bound.

The package is available on pypi, so the simplest way to install it for Python versions 3.6 - 3.11 is to use pip:

.. code-block:: bash

pip3 install low-index

Here is a sample computation:

.. code-block:: python

>>> from low_index import *
>>>  # Conjugacy classes of subgroups of F_3 with index at most 4: 
>>> reps = permutation_reps(rank = 3, short_relators = [], long_relators = [], max_degree = 4)
>>> len(reps)
653
>>> from snappy import *
>>> G = Manifold('K11n34').fundamental_group(); G
Generators:
   a,b,c
Relators:
   aaBcbbcAc
   aacAbCBBaCAAbbcBc
>>> # Degree at most 7 covers of the exterior of the Conway knot:
>>> reps = permutation_reps(G.num_generators(), G.relators()[:1], G.relators()[1:], 7)
>>> len(reps)
52
>>> reps[25]
[[1, 0, 3, 2, 5, 6, 4], [1, 4, 0, 6, 2, 5, 3], [3, 0, 2, 6, 4, 1, 5]]

Credits

Primarily developed by Marc Culler <https://marc-culler.info>, Nathan Dunfield <http://dunfield.info>, and Matthias Goerner <http://www.unhyperbolic.org/>_

License

Copyright 2022 by Marc Culler, Nathan Dunfield, Matthias Goerner and others.

This code is released under the GNU General Public License, version 2 <http://www.gnu.org/licenses/gpl-2.0.txt>_ or (at your option) any later version as published by the Free Software Foundation.