[GAP Forum] DirectFactorsOfGroup

[Horvath Gabor]

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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>
>
> 						Horvath Gabor
> -------------------------------------------------------------------------------
> e-mail:	ghorvath at science.unideb.hu
> phone: +36 52 512900 / 22798
> web: http://www.math.unideb.hu/horvath-gabor


 						Horvath Gabor
-------------------------------------------------------------------------------
e-mail:	ghorvath at science.unideb.hu
phone: +36 52 512900 / 22798
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