Homotopy minimal periods for NR-solvmanifolds maps

A natural number m is called the homotopy minimal period of a map f :X→X if every map g homotopic to f will have periodic points of minimal period m. In this paper we give a complete description of the sets of homotopy minimal periods of a map of compact NR-solvmanifold of dimension ⩾4. In dimension 3 we are able to show this theorem for a map of completely solvable solvmanifold but the description is given as detailed listed table then. This shows that previous results for torus and compact nilmanifold extend to this case.