Solving linear equations over finitely generated abelian groups

Abstract

We discuss various methods and their effectiveness for solving linear equations over finitely generated abelian groups. More precisely, if $\phi :G\to H$ is a homomorphism of finitely generated abelian groups and $b\in H$, we discuss various algorithms for checking whether $b\in \imφ$ holds and if so, for computing a pre-image of $b$ in $G$ together with the kernel of $\phi$.

12 pages; draft