Abstract:We construct new examples of groups with cohomological dimension 2 and geometric dimension 3 with respect to the families of finite subgroups, virtually abelian groups of bounded rank, and the family of virtually poly-cyclic subgroups. Our main ingredients are the examples constructed by Brady-Leary-Nucinckis and Fluch-Leary, and Bass-Serre theory.

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中文翻译：

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集体行动对树木的影响和家庭的艾伦伯格-加涅问题

摘要：关于有限子群族，有界秩的虚拟阿贝尔群和虚拟多环子群族，我们构造了具有同调维度为2和几何维度为3的组的新示例。我们的主要成分是Brady-Leary-Nucinckis和Fluch-Leary以及Bass-Serre理论构建的示例。

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