Projective Special Unitary Group

The projective special unitary group ${\it PSU}_n(q)$ is the Group obtained from the Special Unitary Group ${\it SU}_n(q)$ on factoring by the Scalar Matrices contained in that Group. ${\it PSU}_n(q)$ is Simple except for

$${\it PSU}_2(2) = S_3$$

$${\it PSU}_2(3) = A_4$$

$${\it PSU}_3(2) = 3^2:Q_8,$$

so it is given the simpler name $U_n(q)$, with $U_2(q)=L_2(q)$.

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

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.