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Paper IPM / M / 2350  


Abstract:  
Let μ_{m} be the group of mth roots of unity. In this paper
it is shown that if m is a prime power, then the number of all
square matrices (of any order) over μ_{m} with nonzero constant
determinant or permanent is finite. if m is not a prime power,
we construct an infinite family of matrices over μ_{m} with
determinant one. Also we prove that there is no n×n matrix
over μ_{p} with vanishing permanent, where p is a prime and
n=p^{α}−1.
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