Finite groups with mostly involuted cyclic subgroups
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918140319891456 |
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| author | Chhajer, Vaibhav Sharma, Palash |
| author_facet | Chhajer, Vaibhav Sharma, Palash |
| contents | Let $G$ be a finite group, define $I(G)=\{x\in G : x^{2}=1\}$, $C(G)=$ set of the cyclic subgroups of $G$, $i(G)=|I(G)|$ and $c(G)=|C(G)|$. In this article, we will classify finite groups with $i(G)=c(G)-r$ for $r=0,1,$ and $2$. We also prove that the range of the function given by $β(G)=\frac{i(G)}{c(G)}$ is dense in $[0,1]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00681 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite groups with mostly involuted cyclic subgroups Chhajer, Vaibhav Sharma, Palash Group Theory 20D25, 20E34 Let $G$ be a finite group, define $I(G)=\{x\in G : x^{2}=1\}$, $C(G)=$ set of the cyclic subgroups of $G$, $i(G)=|I(G)|$ and $c(G)=|C(G)|$. In this article, we will classify finite groups with $i(G)=c(G)-r$ for $r=0,1,$ and $2$. We also prove that the range of the function given by $β(G)=\frac{i(G)}{c(G)}$ is dense in $[0,1]$. |
| title | Finite groups with mostly involuted cyclic subgroups |
| topic | Group Theory 20D25, 20E34 |
| url | https://arxiv.org/abs/2508.00681 |