Finite abelian groups via congruences

TL;DR

This paper demonstrates that every finite abelian group can be represented as the multiplicative group of d-th powers modulo some integer n, linking group structure to number theory.

Contribution

It establishes a universal representation of finite abelian groups using congruences and powers, providing a new perspective on their structure.

Findings

Every finite abelian group is isomorphic to a group of d-th powers modulo n.

The representation connects group theory with classical number theory.

Provides a constructive method to realize any finite abelian group through congruences.

Abstract

For every finite abelian group $G$, there are positive integers $n$ and $d$ such that $G$ is isomorphic to the multiplicative group of $d$-th powers of reduced residues modulo $n$.