Thierry Dana-Picard asked:

I know that the Loewy series of a group can be computed with the help
of a certain central series (Jennings's thm).
Is there either some feature in GAP which determines this series for a
given group or somebody who already wrote a GAP program for that
purpose?

There is no function in the present version of GAP to compute the
Jennings series of a p-group or the Loewy series of its group ring,
while in our old system SOGOS we have a command for the computation of
the Jennings series and from it the *dimensions* of the Loewy series.
However both are so easily implemented in GAP that Frank Celler will
do that right now and send you the functions. Also these functions
with full description will probably be put into the next patch. To
compute the Loewy series itself is a different matter, this would
involve computation in the group ring itself and there are no special
provisions for that in GAP at present, so we will not embark on that
now. I hope that perhaps the dimensions will do?

Joachim Neubueser