[GAP Forum] Accessing groups up to isoclinism

[Max Horn]

Dear Vipul,

Am 23.12.2011 um 03:28 schrieb Vipul Naik:

> Dear GAP Forum,
> 
> Two related questions:
> 
> (1) Is there an existing function in GAP or one of the available GAP
> packages to check whether two given finite groups are isoclinic? I
> could write a function, but I'm guessing something already written
> would be more efficient.

The answer to this is "no" to the best of my knowledge. See also
<http://mail.gap-system.org/pipermail/forum/2007/001688.html>
<http://mail.gap-system.org/pipermail/forum/2010/002947.html>


Cheers
Max

> 
> (2) If (1) exists, this can be done in terms of (1), but it would
> still be nice to have this as a standalone: access to the equivalence
> classes of groups of a given order under isoclinism. 
> 
> Background: As I understand, the original classification of groups of
> small prime power orders (e.g., the Hall-Senior classification up to
> 2^6 and the later classification for 2^7) was done by first
> classifying groups up to isoclinism and then finding all the groups
> within a given family of isoclinic groups. However, the ordering of
> groups used by the SmallGroup library is based on somewhat different
> criteria than isoclinism, so all groups in a single family under
> isoclinism do not have adjacent IDs in the SmallGroup librar. I have
> worked out the relation between the SmallGroup IDs and the isoclinism
> families for small prime power orders, but it would be great to be
> able to access the isoclinism information in pre-computed form through
> GAP.
> 
> Vipul
> 
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