  We test several expected isomorphisms between the U(N)xU(N) ABJM theory and
(SU(N)xSU(N))/Z_N theory including the BLG theory by comparing their
superconformal indices. From moduli space analysis, it is expected that this
equivalence can hold if and only if the rank N and Chern-Simons level k are
coprime. We also calculate the index of the ABJ theory and investigate whether
some theories with identical moduli spaces are isomorphic or not.
