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 =2E =2E =2E
Note that this is not a grave problem, since Centralizer (s,s) yields the
desired result in virtually no time.