For finite abelian groups of prime power order the permanent and determinant of the Cayley table have equal numbers of distinct monomials; further equalities and vanishings hold for specific immanants when the order is odd or congruent to 2 mod 4.
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On immanants of Cayley tables
For finite abelian groups of prime power order the permanent and determinant of the Cayley table have equal numbers of distinct monomials; further equalities and vanishings hold for specific immanants when the order is odd or congruent to 2 mod 4.