[GAP Forum] linear groups over ZmodnZ(p^k)

[Hulpke,Alexander]

Dear Forum, Dear Vincent Delecroix,

What GAP does naively, is to compute a permutation action on obits of some basis vectors such that these orbits include a basis. As you have observed, this does not work well for larger residue rings.

You might want to try the matgrp package (which can be found at

https://www.gap-system.org/Packages/matgrp.html

Alas it requires tons of other packages and is subject to these packages modes of operation)

and then call 

FittingFreeLiftSetup

on the group (which will set the groups order). Basically this is the SizeLinearGroupZmodnZ you were looking for.
Email me privately if you have more complicated tasks in mind that do not yet work.

Also, you might be interested in recent joint work of Detinko, Flannery and myself (MR3272380, MR3739225 (also  arXiv:1611.05921v1) and  arXiv:1711.02147v1 )

as well as the associated code at

https://www.dropbox.com/s/i7zgt8879zv7u53/arithmetic.g?dl=0
and its documentation
https://www.dropbox.com/s/ysm73e8a5svho1b/arithmeticdoc.pdf?dl=0

All the best,

  Alexander Hulpke


-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke at colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke