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arXiv · 1809.07191

Characterizations of Cancellable Groups

Matthew Harrison-Trainor·Meng-Che "Turbo" Ho
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Abstract

An abelian group $A$ is said to be cancellable if whenever $A \oplus G$ is isomorphic to $A \oplus H$, $G$ is isomorphic to $H$. We show that the index set of cancellable rank 1 torsion-free abelian groups is $\Pi^0_4$ $m$-complete, showing that the classification by Fuchs and Loonstra cannot be simplified. For arbitrary non-finitely generated groups, we show that the cancellation property is $\Pi^1_1$ $m$-hard; we know of no upper bound, but we conjecture that it is $\Pi^1_2$ $m$-complete.

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BibTeXRIS

Matthew Harrison-Trainor, Meng-Che "Turbo" Ho. 2018-09-19. Characterizations of Cancellable Groups. https://arxiv.org/abs/1809.07191

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