An Arithmetic Characterization of 2-Generated Numbers
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908499133333504 |
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| author | Das, Bireswar Samant, Kavita Thakkar, Dhara |
| author_facet | Das, Bireswar Samant, Kavita Thakkar, Dhara |
| contents | A group $G$ is said to be $k$-generated if it has a generating set with $k$ elements. A positive integer $n$ is called a \emph{2-generated number} if every group of order $n$ is 2-generated. In this article, we establish an arithmetic characterization of 2-generated numbers expressed in terms of the prime factorization of $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_16356 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Arithmetic Characterization of 2-Generated Numbers Das, Bireswar Samant, Kavita Thakkar, Dhara Group Theory 20D60, 20F05, 05C25 A group $G$ is said to be $k$-generated if it has a generating set with $k$ elements. A positive integer $n$ is called a \emph{2-generated number} if every group of order $n$ is 2-generated. In this article, we establish an arithmetic characterization of 2-generated numbers expressed in terms of the prime factorization of $n$. |
| title | An Arithmetic Characterization of 2-Generated Numbers |
| topic | Group Theory 20D60, 20F05, 05C25 |
| url | https://arxiv.org/abs/2508.16356 |