An Arithmetic Characterization of 2-Generated Numbers

2025/08/22 by Das, Bireswar, Samant, Kavita, Thakkar, Dhara
#05C25 #20D60 #20F05 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2508.16356

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 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.

Citations

• CLT-groups with cyclic or abelian subgroups

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