Actually, let me correct myself.
Current implementation is based on some tweaks and then computing all
normal subgroups, because most of the cases the Kayal-Nezhmetdinov
algorithm performed slower. That algorithm can still be called with the
useKN option if someone wants to.
As I see, though, Chris Jefferson recently has published an algorithm for
permutation groups given by generators. Not sure if that is implemented in
some package, though.
https://www.sciencedirect.com/science/article/abs/pii/S0747717121000274
Thanks,
Gábor
On Thu, 17 Feb 2022, Horvath Gabor wrote:
Dear Bob,
You are correct, there is no documentation for this function, because indeed,
originally it was developed for StructureDescription.
However, it's output should be valid. The only possible concern is the
running time. Though for small groups library I would expect it to produce
results reasonably quick (say <1 hour on some new hardware even in the worst
case), unless it is some huge nilpotent group.
The current implementation uses the Kayal-Nezhmetdinov algorithm, together
with some tweaks that try to figure out early on in some cases if the group
is indecomposable.
https://www.semanticscholar.org/paper/Factoring-Groups-Efficiently-Kayal-Nezhmetdinov/d37fa0e6307a8de1f5d927efbb66817486fbf289
Thanks,
Gábor
On Thu, 17 Feb 2022, Bob Heffernan wrote:
Dear all,
I want to check whether a group is indecomposable (i.e. it cannot be
written as a direct product of smaller groups). I'm making use of the GAP
function DirectFactorsOfGroup, so a group is indecomposable if the list
returned by this function has length 1.
This function is, however, undocumented. My understanding is that it
exists to be used by StructureDescription. The documentation for
StructureDescription mentions that it is primarily intended for small
groups (of order less than 100) and I know it is intended as an educational
tool more than anything else.
So, it is possibly the case that DirectFactorsOfGroup is intended only to
be "good enough" for the purposes of StructureDescription and it might be
that I shouldn't trust it too far.
The groups I'm looking at are all in the library of small groups, so they
are "small" in that sense, but have orders larger than 100.
Can anybody shed any light on this?
Thank you & best regards,
Bob Heffernan
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