GROUPS HAVING 12 CYCLIC SUBGROUPS Article Swipe
Related Concepts
Mathematics
Cyclic group
Pure mathematics
Abelian group
K.L. Sharma
,
A. Satyanarayana Reddy
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.1017/s0004972725100427
· OA: W4413628465
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.1017/s0004972725100427
· OA: W4413628465
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].
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