Finite non-cyclic nilpotent group whose number of subgroups is minimal
2021
Let G be a finite group and $$\mathfrak {s}(G)$$
denote the number of subgroups of G. Aivazidis and Muller proved that if G is a non-cyclic p-group of order $$p^{\lambda }$$
, then $$\mathfrak {s}(G)\ge 6$$
whenever $$p^{\lambda }=2^3$$
; $$s(G)\ge (p+1)(\lambda -1)+2$$
whenever $$p^{\lambda }\ne 2^3$$
. In this paper, we generalize the results of Aivazidis and Muller on all finite non-cyclic nilpotent groups. Lower bounds on $$\mathfrak {s}(G)$$
of non-cyclic nilpotent groups G are established.
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