A note on fundamental group lattices

TL;DR

This paper offers a new proof of a classical result concerning projectivities between finite abelian groups, utilizing the concept of fundamental group lattice, and extends this result to a broader context.

Contribution

It introduces a novel proof approach based on fundamental group lattices and generalizes existing results about projectivities in finite abelian groups.

Findings

New proof of classical projectivity result

Extension of the result to a more general setting

Enhanced understanding of fundamental group lattices

Abstract

The main goal of this note is to provide a new proof of a classical result about projectivities between finite abelian groups. It is based on the concept of fundamental group lattice, studied in our previous papers \cite{8} and \cite{9}. A generalization of this result is also given.