  Ore proved that a finite group is cyclic if and only if its subgroup lattice
is distributive. Now, since every subgroup of a cyclic group is normal, we call
a subfactor planar algebra cyclic if all its biprojections are normal and form
a distributive lattice. The main result generalizes one side of Ore's theorem
and shows that a cyclic subfactor is singly generated in the sense that there
is a minimal 2-box projection generating the identity biprojection. We
conjecture that this result holds without assuming the biprojections to be
normal, and we show that it is true for small lattices. We finally exhibit a
dual version of another theorem of Ore and a non-trivial upper bound for the
minimal number of irreducible components for a faithful complex representation
of a finite group.
