> < ^ Date: Fri, 11 Jul 1997 18:24:29 +1000
> < ^ From: Burkhard Hoefling <b.hoefling@tu-bs.de >
> ^ Subject: function 'Centre' for special Ag groups

Dear Forum members,

I would like to point out the following problem with the function 'Centre'
for special Ag groups: sometimes, the maximum size of a field in GAP is not
large enough to compute the centre of even a small special Ag group with
the function 'Centre'. The group in the following example has order
216=3D2^3.3^3. It is, in fact, a central product of SL(2,3) with a cyclic
group of order 18.

g :=3D Group( [ [ E(4), 0 ], [ 0, -E(4) ] ],
   [ [ 1/2*E(108)^56-1/2*E(108)^83, 1/2*E(108)^56-1/2*E(108)^83 ],
     [ -1/2*E(108)^56-1/2*E(108)^83, 1/2*E(108)^56+1/2*E(108)^83 ] ] );
a :=3D AgGroup (g);
s :=3D SpecialAgGroup (a);
Centre (s);

results in the following error message:

Error, Z: <q> must be a prime power in [2..65536] at
return Z( p ^ d ) ^ i ... in

Note that this is not a grave problem, since Centralizer (s,s) yields the
desired result in virtually no time.

Best regards,
Burkhard Hofling.

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