论文标题
Schur和Baer定理的一些概括及其与同源代数的联系
Some generalisations of Schur's and Baer's theorem and their connection with homological algebra
论文作者
论文摘要
Schur的定理及其概括Baer的定理在群体理论中是显着的结果，将上部中央商与下中央系列联系起来。本文的目的是使用与非亚洲张量产品相关的新方法将这些结果概括为两个不同的方向。特别是，我们为有限生成的组证明了Schur-Baer定理的一个版本。然后，我们应用这些新获得的结果来描述$ k $ nilpotent乘数，以$ k \ geq 2 $和其他不变的组。
Schur's Theorem and its generalisation, Baer's Theorem, are distinguished results in group theory, connecting the upper central quotients with the lower central series. The aim of this paper is to generalise these results in two different directions, using novel methods related with the non-abelian tensor product. In particular, we prove a version of Schur-Baer Theorem for finitely generated groups. Then, we apply these newly obtained results to describe the $k$-nilpotent multiplier, for $k\geq 2$, and other invariants of groups.
