[GAP Forum] testing for membership of Omega+/-

[Leonard Soicher]

Dear Derek, Dear GAP-Forum,

See the "ATLAS of Finite Groups" Introduction, especially the last
three paragraphs of page xi and then first two paragraphs of page xii.
I believe the nice method for even q (and even d), using the dimension of the 
fixed space, was discovered by Richard Parker and proved by John Conway,
but I know of no published proof.

Regards, 
Leonard Soicher

On Fri, Oct 21, 2005 at 06:03:02PM +0100, Derek Holt wrote:
> Dear GAP Forum,
> 
> Does anybody know of any algorithms, or preferably implementations of
> algorithms, for testing whether a matrix in SO^{+/-}(d,q) (d even) lies
> in the perfect subgroup of index two, Omega^{+/-}(d,q) ?
> 
> There are quick one-sided Monte-Carlo algorithms for verifying that an element
> in a finite group G lies in the commutator subgroup [G,G], which one could
> use to get an answer with a small probability of it being incorrect, but
> surely there must be a deterministic method of deciding this.
> 
> Thanks,
> Derek Holt.
> 
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