An Arithmetic Characterization of 2-Generated Numbers

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 $n$.

15 pages, accepted for publication in Proceedings-Mathematical Sciences