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Split orthogonal group over a finite field


I want to use the split orthogonal group in simulations (explicit description at wiki page “ Indefinite orthogonal group”) over a finite field (\mathbb{F}_p).

I was able to get classical groups that leave a bilinear form invariant, though was not able to enter a general form (and in particular the form that the split orthogonal group leaves invariant)

Thanks in advance