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arXiv · 2512.24318

Isomorphism types of definable (maximal) cofinitary groups

Lukas Schembecker
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Abstract

Kastermans proved that consistently $\bigoplus_{\aleph_1} \mathbb{Z}_2$ has a cofinitary representation. We present a short proof that $\bigoplus_{\mathfrak{c}} \mathbb{Z}_2$ always has an arithmetic cofinitary representation. Further, for every finite group $F$ we construct an arithmetic maximal cofinitary group of isomorphism type $(\ast_{\mathfrak{c}} \mathbb{Z}) \times F$. This answers an implicit question by Schrittesser and Mejak whether one may construct definable maximal cofinitary groups not decomposing into free products.

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Lukas Schembecker. 2025-12-30. Isomorphism types of definable (maximal) cofinitary groups. https://arxiv.org/abs/2512.24318

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