General Orthogonal Group

The general orthogonal group ${\it GO}_n(q,F)$ is the Subgroup of all elements of the Projective General Linear Group that fix the particular nonsingular Quadratic Form $F$. The determinant of such an element is $\pm 1$.

See also Projective General Linear Group

References

Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; and Wilson, R. A. ``The Groups ${\it GO}_n(q)$, ${\it SO}_n(q)$, ${\it PGO}_n(q)$, and ${\it PSO}_n(q)$, and ${\it O}_n(q)$.'' §2.4 in Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups. Oxford, England: Clarendon Press, pp. xi-xii, 1985.