[GAP Forum] Canonical form for some small groups and efficient characterisation of the generalized symmetric groups

[Horvath Gabor]

I am not sure if this helps you, but maybe check out StructureDescription:

https://www.gap-system.org/Manuals/doc/ref/chap39.html#X87BF1B887C91CA2E

Best,
Gabor

On Sun, 17 Dec 2017, Martin Rubey wrote:

> Dear Josh, Dear Forum,
>
> Joshua Hunt <joshuahunt at math.ku.dk> writes:
>
>> I'm afraid I don't quite understand your objection to the SmallGroup
>> library. What requirements does it not fulfil?
>
> Essentially: it doesn't cover S_7, S_5 § Z_2, etc.
>
> So: the small group ID is just perfect for the "small" objects, but it
> simply doesn't work for enough groups obtained as images of maps from,
> say, graphs to groups.
>
> In fact, that's what you write here:
>
>> I would also point out that "groups of order less than 47" doesn't
>> cover a lot of groups you probably would care about
>> (e.g. symmetric/alternating groups S_5/A_5 and bigger, as mentioned
>> in your example).
>
> Let me try to put it in different words:
>
> when initialising the findstat database,
>
> * first we compute the canonical forms of the small objects (for groups:
>  order less than 47)
> 
> * then we apply the maps in the database (eg, "automorphism group of a
>  graph", "Weyl group of a finite Cartan type", "center of a group"),
>  and compositions of two and three maps, to all small objects (eg,
>  graphs, finite Cartan types, groups,...), and compute canonical forms
>  of those.
>
> Does this make it clearer?
>
> Best,
>
> Martin
>
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 						Horvath Gabor
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