Chebotarev type results for composite group order Part 1: square free natural numbers

Abstract: Chebotarev's Fourier minor theorem states that all minors of discrete Fourier matrices of prime order are nonzero. This property only holds in the prime order case, but for some composites it can be shown that at least all principal minors are nonzero. To establish such cases for square free composites is the goal of this paper. In a subsequent paper we discuss composites containing squares.