The equivalence of two cyclic objects on pq elements Original Research Article

Pálfy showed that two equivalent cyclic objects on n elements are equivalent by a multiplier provided gcd(n, ϕ(n)) = 1 or n = 4. He also showed that there exist equivalent cyclic objects on n elements that are not multiplier equivalent when gcd(n, ϕ(n)) ≠ 1 and n ≠ 4. Huffman et al. (1993) showed that when n = p2, p an odd prime, two equivalent cyclic objects on n elements are equivalent by elements chosen from a list of at most ϕ(n) permutations. In this paper we show that when n = pq, p and q primes, with gcd(pq, ϕ(pq)) ≠ 1, two equivalent cyclic objects on n elements are equivalent by elements chosen from a list of at most ϕ(n) permutations. In fact, these permutations are products of multipliers and “pieces” of multipliers.