We describe an algorithm to find the virtual cohomological dimension of the automorphism group of a right‐angled Artin group. The algorithm works in the relative setting; in particular, it also applies to untwisted automorphism groups and basis‐conjugating automorphism groups. The main new tool is the construction of free abelian subgroups of certain Fouxe–Rabinovitch groups of rank equal to their virtual cohomological dimension, generalizing a result of Meucci in the setting of free groups.

中文翻译：

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计算RAAG自同构群的虚拟同调维

我们描述了一种算法，该算法可找到直角Artin组自同构组的虚拟同调维。该算法在相对设置下工作；特别是，它也适用于未扭曲的自同构群和基共轭自同构群。主要的新工具是构造某些等级等于其虚拟同调维数的Foux–Rabinovitch群的自由阿贝尔子群，从而推广了Meucci在自由群环境中的结果。