Solving linear equations over finitely generated abelian groups

Ren\'e Hartung

Solving linear equations over finitely generated abelian groups

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arxiv 1007.2477 v1 pith:UFR67YYE submitted 2010-07-15 math.GR

Solving linear equations over finitely generated abelian groups

Ren\'e Hartung This is my paper

classification math.GR

keywords abelianfinitelygeneratedgroupsvarphidiscussequationslinear

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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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