  An action of a compact, in particular finite group on a C*-algebra is called
properly outer if no automorphism of the group that is distinct from identity
is implemented by a unitary element of the algebra of local multipliers of the
C*-algebra and strictly outer if the commutant of the algebra in the algebra of
local mutipliers of the cross product consists of scalars [11]. In [11, Theorem
11] I proved that for finite groups and prime C*-algebras (not necessarily
separable), the two notions are equivalent. I also proved that for finite
abelian groups this is equivalent to other relevant properties of the action
[11 Theorem 14]. In this paper I add other properties to the list in [11,
Theorem 14].
