Lower Bounds on the Number of Cyclic Subgroups in Finite Non-Cyclic Nilpotent Groups

Abstract

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.