Solving linear equations over finitely generated abelian groups

Details Solving linear equations over finitely generated abelian groups Solving linear equations over finitely generated abelian groups

2010-07-15

arxiv.org/abs/1007.2477v1

Mathematics

Group Theory

12 pages; draft

Scientific paper

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

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