C2-Cofiniteness of 2-Cyclic Permutation Orbifold Models

In this article, we consider permutation orbifoldmodels of C-2-cofinite vertex operator algebras of CFT type. We show the C-2-cofiniteness of the 2-cyclic permutation orbifold model (V circle times V)(S2) for an arbitrary C-2-cofinite simple vertex operator algebra V of CFT type. We also give a proof of the C-2-cofiniteness of a Z(2)-orbifold model V-L(+) of the lattice vertex operator algebra V-L associated with a rank one positive definite even lattice L by using our result and the C-2-cofiniteness of V-L.