© 2019 Topology Proceedings. Define the following order among all natural numbers except for 2 and 1: 4 ≫ 6 ≫ 3 ≫ · · · ≫ 4n ≫ 4n + 2 ≫ 2n + 1 ≫ 4n + 4 ≫... Let f be a continuous interval map. We show that if m ≫ s and f has a cycle with no division (no block structure) of period m, then f has also a cycle with no division (no block structure) of period s. We describe possible sets of periods of cycles of f with no division and no block structure.
