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GROUPS HAVING 12 CYCLIC SUBGROUPS
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society , First View
- Published online by Cambridge University Press:
- 26 August 2025, pp. 1-12
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- Article
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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].
