> < ^ From:

< ^ Subject:

Dear Gap Forum,

Burkhard H"ofling wrote:

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 =2ENote that this is not a grave problem, since Centralizer (s,s) yields the

desired result in virtually no time.

Unfortunately, it is a feature of the underlying algorithm that it

needs large finite fields. Since GAP can only deal with finite

fields of size < 2^16 at the moment, the algorithm will run in an

error if it needs larger fields.

However, the underlying algorithm SagGroupOps.Centre is often faster

than the generic method AgGroupOps.Centre and the above bug does not

turn up very often. This is the reason why the algorithm is still

used as SagGroupOps.Centre.

Best wishes, Bettina

> < [top]