Constructing groups of type $FP_2$ over fields but not over the integers

preprint2021arXivOpen access

We construct examples of groups that are $FP_2(\mathbb{Q})$ and $FP_2(\mathbb{Z}/p\mathbb{Z})$ for all primes $p$ but not of type $FP_2(\mathbb{Z})$ .

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Constructing groups of type $FP_2$ over fields but not over the integers

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Constructing groups of type FP2FP_2FP2​ over fields but not over the integers

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Constructing groups of type $FP_2$ over fields but not over the integers