[GAP Forum] groups of order p^3*q^3

[Alexander Konovalov]

Dear Walter, dear GAP Forum,

> On 25 Jul 2016, at 15:02, Alexander Konovalov <alexander.konovalov at st-andrews.ac.uk> wrote:
> 
> Dear Walter,
> 
>> On 25 Jul 2016, at 14:45, Walter Becker <w_becker at hotmail.com> wrote:
>> 
>> The question is how many groups are there for these
>> orders.  Note here that the Group Constructions program
>> of  Besche and Eick give for the case of p=3 and q=7 the
>> number 215 (and actually constructs them). The Thesis of
>> of R. Laue (see page 226) seems to give 229 (plus the
>> 25 direct product cases of the groups of order 27 and 343 ?).
>> 
>> The compiled list of groups available on the internet does
>> not contain an entry for the groups of order 9261.
> 
> The Group Numbers reproducibility project 
> (https://github.com/alex-konovalov/gnu)
> actually has an entry for gnu(9261): see
> 
> https://github.com/alex-konovalov/gnu/pull/43
> 
> and it is 215. Same number obtained by using the
> latest GrpConst package both in GAP 4.8.3 and master
> branch of the development version of GAP at the
> time of submission.
> 
> I don't have Laue's thesis so I can not comment more
> on the reasons for the discrepancies, but hopefully
> some one else could add more.

I was pointed out (thanks!) that the reader who is not 
familiar with the Group Numbers reproducibility project 
may read my email as a confirmation of an independent 
count of groups of order 9261, what is not true - it was
counted using the same approach used by Walter (using the 
GrpConst package) - what I had in mind replying to Walter
was to confirm that the same number is replicated in other 
calculations and is actually reported somewhere on the internet.

Having an independent count produced by other implementations
or by purely theoretical calculations is certainly interesting.

Actually, in the Group Numbers reproducibility project there 
are several categories (GitHub labels) for gnu(n) entries to 
specify different levels of their reproducibility:

* replicated: the same count is obtained using the same code 
on a different machine, possibly with different versions of 
the software (but calling the same GAP functions).

* reproduced: the same count is obtained using another 
implementation (for example, for cubefree groups one 
could use the GrpConst package and the Cubefree package)

* agrees with theory: the count is checked against the literature

Hopefully more labels of the latter two kinds will appear at 
some point.

Best wishes
Alexander