[GAP Forum] DirectFactorsOfGroup

[Horvath Gabor]

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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 						Horvath Gabor
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