In this paper we give a complete result for calculating the Nielsen-Jiang periodic numbers NFn(f) and NPn(f) of self maps f of infra-solvmanifolds of type (R). We show that infra-solvmanifolds of type (R) are essentially reducible to the GCD and essentially toral, and determine conditions under which NFn(f) = N(fn). We also show that the prime Nielsen-Jiang periodic number NPn(f) can be calculated by the holonomies of the manifolds. This shows that previous results for infra-nilmanifolds extend to this case. (c) 2023 Published by Elsevier B.V.
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