Ruth Schwingel asked:
> Given a module M acted on by an algebra A the function
> 'CompositionFactors' determines the modules which are
> the actions of A on the factors of a composition series.
> Is it also possible to determine the actual composition
> series as a list of (bases for the) submodules?
There is no user-interfaced function in GAP3 that will return the submodules.
The functionality exists in principle somewhere (it is used in `ChiefSeries'
for solvable groups) but in GAP3 it would be a mess to call. (This was one of
the reasons for changes in GAP4.)
If you want, I can send you privately some code that (together with the
Matrix share package) will permit to compute bases for the submodules in a
composition series. This function is also available in GAP4, again I can
tell you how to call it.