Automorphically Equivalent Elements of Finite Abelian Groups

Arjun Agarwal, Rachel Chen, Rohan Garg +1

Given a finite abelian group $G$ and elements $x,y\in G$, we prove that there exists $\varphi \in \text{Aut}(G)$ such that $\varphi (x)=y$ if and only if $G/\langle x \rangle \cong G/\langle…