  We prove the Landau-Ginzburg Mirror Symmetry Conjecture at the level of
(orbifolded) Frobenius algebras for a large class of invertible singularities,
including arbitrary sums of loops and Fermats with arbitrary symmetry groups.
Specifically, we show that for a quasi-homogeneous polynomial W and an
admissible group G within the class, the Frobenius algebra arising in the FJRW
theory of [W/G] is isomorphic (as a Frobenius algebra) to the orbifolded Milnor
ring of [W^T/G^T], associated to the dual polynomial W^T and dual group G^T.
