Projective Special Orthogonal Group

The projective special orthogonal group ${\it PSO}_n(q)$ is the Group obtained from the Special Orthogonal Group ${\it SO}_n(q)$ on factoring by the Scalar Matrices contained in that Group. In general, this Group is not Simple.

See also Projective Special Linear Group, Projective Special Unitary Group, Special Orthogonal 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.