Construction of Several Classes of Single-cycle Polynomials over Z/(pn)

This paper studies single-cycle polynomials over the integer residue ring Z/(pn) with prime p5 and integer n2, and presents several classes of such single-cycle polynomials. As the research of single-cycle polynomials over Z/(pn) can be reduced to the case over Z/(p2), an exact characterization of single-cycle polynomials over Z/(5) is given in terms of their coefficients, and then a complete characterization of single-cycle polynomials of degree 6 over Z/(52) is given based on it. In addition, a partial construction of single-cycle polynomials of degree (p1) over Z/(p2) is also proposed.