(untitled) (Journal of Mathematical Study, 2023)
Let G be a finite group and c(G) denote the number of cyclic subgroups of G. It is known that the minimal value of c on the set of groups of order n, where n is a positive integer, will occur at the cyclic group Z_n. In this paper, for non-cyclic nilpotent groups G of order n, the lower bounds of c(G) are established.