Abstract
Recently, a formula for computing the Nielsen periodic numbers NFn(f) and NPn(f) of self maps f on infra-nilmanifolds and infra-solvmanifolds of type (R) was found. In this paper, we extend this formula to the case of general infra-solvmanifolds. We show that infra-solvmanifolds are essentially reducible to the GCD and essentially toral, and determine conditions under which NFn(f)=N(fn). We show that the prime Nielsen-Jiang periodic number NPn(f) of a self map f on an infra-solvmanifold M can be calculated by Nielsen numbers of lifts of suitable iterates of f to an NR-solvmanifold that finitely covers M.
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