We say a group G satisfies properties (M) and (NM) if every nontrivial finite subgroup of G is contained in a unique maximal finite subgroup, and every nontrivial finite maximal subgroup is self-normalizing. We prove that the Bredon cohomological dimension and the virtual cohomological dimension coincide for groups that admit a cocompact model for EG and satisfy properties (M) and (NM). Among the examples of groups satisfying these hypothesis are cocompact and arithmetic Fuchsian groups, one-relator groups, the Hilbert modular group, and 3-manifold groups.

中文翻译：

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关于在其有限子群上满足某些条件的群的维数

我们说一组G如果每个非平凡有限子群满足性质 (M) 和 (NM)G包含在一个唯一的极大有限子群中，并且每个非平凡有限极大子群都是自归一化的。我们证明 Bredon 上同调维数和虚拟上同调维数对于承认协紧模型的群是一致的乙G并满足性质 (M) 和 (NM)。满足这些假设的群的例子有协紧和算术 Fuchsian 群、单相关者群、希尔伯特模群和 3-流形群。