  BHK mirror symmetry as introduced by Berglund--H\"ubsch and Marc Krawitz
between Landau--Ginzburg (LG) models has been the topic of much study in recent
years. An LG model is determined by a potential function and a group of
symmetries. BHK mirror symmetry is only valid when the group of symmetries is
comprised of the so-called diagonal symmetries. Recently, an extension to BHK
mirror symmetry to include nonabelian symmetry groups has been conjectured. In
this article, we provide a mirror map at the level of state spaces between the
LG A-model state space and the LG B-model state space for the mirror model
predicted by the BHK mirror symmetry extension for nonabelian LG models. We
introduce two technical conditions, the Diagonal Scaling Condition, and the
Equivariant $\Phi$ condition, under which a bi-degree preserving isomorphism of
state spaces (the mirror map) is guaranteed to exist, and we prove that the
condition is always satisfied if the permutation part of the group is cyclic of
prime order.
