Groups having 12 cyclic subgroups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866908876547293184 |
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| author | Sharma, Khyati Reddy, A. Satyanarayana |
| author_facet | Sharma, Khyati Reddy, A. Satyanarayana |
| contents | 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 $cdeg (G)$. 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 gives a solution to the problem asked by Tărnăuceanu and Tóth in [20] "For every $a\in [0, 1]$, does there exist a sequence $(G_n)$ of finite groups such that $\lim_{n\to\infty} cdeg(G_n)=a$ "? |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_11788 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Groups having 12 cyclic subgroups Sharma, Khyati Reddy, A. Satyanarayana Combinatorics Group Theory 20D60, 20D25, 20D20 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 $cdeg (G)$. 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 gives a solution to the problem asked by Tărnăuceanu and Tóth in [20] "For every $a\in [0, 1]$, does there exist a sequence $(G_n)$ of finite groups such that $\lim_{n\to\infty} cdeg(G_n)=a$ "? |
| title | Groups having 12 cyclic subgroups |
| topic | Combinatorics Group Theory 20D60, 20D25, 20D20 |
| url | https://arxiv.org/abs/2210.11788 |