[GAP Forum] Numbering of primitive groups

[Alexander Hulpke]

Dear Peter, Dear Forum,

> Akos Seress, in Bull. London Math. Soc. 29 (1997), 697-704, listed all the
> (finitely many) primitive groups which have no regular orbit on the power
> set of their domain. He listed them by GAP number and ATLAS name.
> 
> Sad to say, the GAP numbering seems to have changed since then. For
> example, Akos thought PrimitiveGroup(16,19) is 2^4.A_7, whereas GAP now
> thinks this group is 2^4.A_5.
> 
> I have two questions:
> 1. Does anyone have a list correlating the old and new numbers? I think
> that, from the ATLAS names, I can recover what he meant, but it would be
> nice to have a check.

From the publication date and the citation in the paper I presume that Akos' list was done using GAP3. I append a renumbering of the groups that gives for degrees up to 50 the *new* number for each group. (I believe the reason for renumbering had to do with storing primitive groups in cohorts according to the ONan-Scott Theorem, but I might be remembering wrongly.)
For example in this list, entry 16,19 is 20, i.e. the group formerly numbered 16,19 is nor 16,20.

The reverse permutation is available in GAP via the function SimsNo, that when applied to a primitive group return the old index. E.g.:

gap> SimsNo(PrimitiveGroup(16,20));
19

as expected.

Best,

  Alexander


>  
> 2. Is there any way that we can draw the group-theory community's
> attention to this, perhaps with an updated list?
> 
> Peter.
> 

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