Addendum to “Finite groups with a prescribed number of cyclic subgroups”

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

“…Regarding the results about c(G) =|G|−r. Belshoff, Dillstrom and Reid [2,3] established a more remarkable bound. They showed that |G| ≤ 8r.…”