In this article, we study isomorphisms between simple current extensions of a simple VOA. For example, we classify the isomorphism classes of simple current extensions of the VOAs and where Λ16 is the Barnes-Wall lattice of rank 16. Moreover, we consider the same simple current extension and describe the normalizer of the abelian automorphism group associated with this extension. In particular, we regard the moonshine module as simple current extensions of five subVOAs for 2-elementary totally even lattices L, and describe corresponding five normalizers of elementary abelian 2-group in the automorphism group of in terms of by using this description, we show that three of them form a Monster amalgam.
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