> < ^ Date: Wed, 21 Aug 1996 11:50:40 +0200
> < ^ From: Alexander Hulpke <hulpke@math.colostate.edu >
^ Subject: Re: [no subject] (transitive groups of degree 12)

Dear GAP-Forum,

Mario Pineda Ruelas asked,

Few days ago I have obtained GAP from internet and I have printed the
manual GAP. I find in the references of the manual GAP the next paper:

Gordon F. Royle. The transitive groups of degree twelve,
J. Symbolic Computation, pages 255-268,1987.

wich I suppose that is incrporated to GAP.
In this paper we can find that Mr. Royle gives a imprimitive group of order
252900 which contain the prime divisor 281(page 265). As you can see this
is imposible because this group is contained in S_12.
I think that the order of this group must be 259200.

You're right. Its A6\wr 2. I think when creating the table this typo crept in.
You could use a 'for' loop in GAP and the command 'AllBlocks' to recreate a
similar list without human interference if you suspect further errors.

?are there another involuntary mistakes in the paper of Mr. Royle

I must admit that I never checked the exact numbers given in the paper, but
used a list derived from Mr. Royles original results instead. To my
knowledge this list is correct (see also below).
I have read Royle's paper and I can assure you that the paper's argumentation
is correct. I have not double checked, however, whether the numbers given in
the tables contain any other typographical mistakes.

I like know if the information contained in the paper of Mr.Royle are the
same that GAP.

Essentially yes. But they were derived from the original data lists without

Additionally, for my PhD I constructed the transitive groups of degree up
to 31 from scratch, also constructing the groups of degree up to 15 anew.
There were no discrepancies with GAP's lists. Thus I am *VERY* certain that
these lists as given in GAP are correct.

If you are interested you can find further information on my WWW page
Incidentally, this page also contains a link to a joint preprint that lists
all transitive groups of degree up to 15 with some of their properties.
These lists were created without retyping, thus I'm quite confident
about their correctness.

> ?is there anyone in the Forum that can tell me how to obtain from GAP a
> list of imprimitive groups of degree twelve.

Starting with version 3.4, patchlevel 3 (released in last december) GAP
contains the transitive groups of degree up to 15. The command
'AllTransitiveGroups(DegreeOperation,12,IsPrimitive,false)' yields a list of
these groups. The manual section 'The Transitive Groups Library' gives
further information in case you want to get subsets with other properties.

Hope this is of help,

Alexander Hulpke

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