Factorization numbers of finite rank $3$ abelian $p$-groups

TL;DR

This paper provides a formula for the factorization number of finite rank 3 abelian p-groups, extending previous results and contributing to the understanding of their algebraic structure.

Contribution

It introduces a new formula for the factorization number of rank 3 abelian p-groups, expanding prior work in the field.

Findings

Derived a formula for F_2(G) for rank 3 abelian p-groups

Extended previous results to a broader class of groups

Contributed to the theoretical understanding of group factorizations

Abstract

In this short note we give a formula for the factorization number $F_2(G)$ of a finite rank $3$ abelian $p$-group $G$. This extends a result in our previous work \cite{9}.