发表机构
State University of Campinas (UNICAMP)（坎皮纳斯州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明多种群类（偶数Artin群、RAAG、极限群、Coxeter群、可解群、广义Baumslag-Solitar群及$SL_n(\Z)$等）的非交换外平方的剩余有限性，并建立上同调与同调良性的等价性。
AI 中文摘要
我们证明了上同调良性与同调良性是等价的。我们证明，若$G$是一个凝聚偶数Artin群，或其底图不含4团，或是一个LERF Artin群，则$G \otimes G$和$G \wedge G$是剩余有限的。此外，对于$G$为RAAG（右角Artin群），对任意素数$p$，$G \otimes G$和$G \wedge G$都是剩余$p$-有限的。对于$G$为极限群或Coxeter群，我们证明$G \wedge G$是剩余有限的。对于$G$为$FP_{\infty}$型可解群，我们证明群$\X(G)$、$\nu(G)$、$G \wedge G$对几乎所有素数$p$都是几乎剩余$p$-有限的。对于$G$为秩$n \geq 1$的剩余有限广义Baumslag-Solitar群，我们证明$G \wedge G$是剩余有限的。对于$G = SL_n(\Z)$和$G = GL_n(\mathbb{Z})$，$n \geq 3$，我们证明$G \wedge G$是剩余有限的。
英文摘要
We show that cohomological and homological goodness are equivalent. We prove that if $G$ is a coherent even Artin group or an even Artin group whose underlying graph does not contain 4-clique or a LERF Artin group then $G \otimes G$ and $G \wedge G$ are residually finite. Furthermore for $G$ a RAAG both $G \otimes G$ and $G \wedge G$ are residually $p$-finite for any prime integer $p$. For $G$ a limit group or a Coxeter group we show that $G \wedge G$ is residually finite. For $G$ a soluble group of type $FP_{\infty}$ we prove that the groups $\X(G)$, $ν(G)$, $G \wedge G$ are virtually residually $p$-finite for almost all primes $p$. For $G$ a generalised Baumslag-Solitar group of rank $n \geq 1$ that is residually finite, we show that $G \wedge G$ is residually finite. For $G = SL_n(\Z)$ and $G = GL_n( \mathbb{Z})$, $n \geq 3$, we show that $G \wedge G$ is residually finite.
