GROUPS HAVING 12 CYCLIC SUBGROUPS

Abstract A finite group is said to be n-cyclic if it contains n cyclic subgroups. For a finite group G , the ratio of the number of cyclic subgroups to the number of subgroups is known as the cyclicity degree of the group G and is denoted by $\textit {cdeg} (G)$ . In this paper, we classify all $12$ -cyclic groups. We also prove that the set of cyclicity degrees for all the finite groups is dense in $[0,1]$ , which solves a problem posed by Tărnăuceanu and Tóth [‘Cyclicity degrees of finite groups’, Acta Math. Hungar. 145 (2) (2015), 489–504].