General Unitary Group

The general unitary group ${\it GU}_n(q)$ is the Subgroup of all elements of the General Linear Group ${\it GL}(q^2)$ that fix a given nonsingular Hermitian form. This is equivalent, in the canonical case, to the definition of ${\it GU}_n$ as the group of Unitary Matrices.

References

Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; and Wilson, R. A. ``The Groups ${\it GU}_n(q)$, ${\it SU}_n(q)$, ${\it PGU}_n(q)$, and ${\it PSU}_n(q)={\it U}_n(q)$.'' §2.2 in Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups. Oxford, England: Clarendon Press, p. x, 1985.