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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.

Best regards,

Burkhard Hofling.

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