  We introduce a class of automorphisms of compact quantum groups which may be
thought of as inner automorphisms and explore the behaviour of normal subgroups
of compact quantum groups under these automorphisms. We also define the notion
of center of a compact quantum group and compute the center for several
examples. We briefly touch upon the commutator subgroup of a compact quantum
group and discuss how its relation with the center can be different from the
classical case.
