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

[Derek Holt]

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.