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arXiv · 2508.16356

An Arithmetic Characterization of 2-Generated Numbers

Bireswar Das·Kavita Samant·Dhara Thakkar
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Abstract

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 $n$.

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Bireswar Das, Kavita Samant, Dhara Thakkar. 2025-08-22. An Arithmetic Characterization of 2-Generated Numbers. https://arxiv.org/abs/2508.16356

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