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We prove that if G is an abelian group of odd order then there is anisomorphism from the second quandle homology of the Takasaki quandle of G tothe exterior square of G. In particular, for G=Z_k^n, k odd, we obtainZ_k^{n(n-1)/2}. Nontrivial second homology allows us to use 2-cocycles toconstruct new quandles from T(G), and to construct link invariants.

THE SECOND QUANDLE HOMOLOGY OF THE TAKASAKI QUANDLE OF AN ODD ABELIAN GROUP IS AN EXTERIOR SQUARE OF THE GROUP