Schur和Baer定理的推广及其与同调代数的联系
Some generalisations of Schur's and Baer's theorem and their connection with homological algebra
摘要：
舒尔定理和它的推广，贝尔定理，是杰出的结果在群论，连接的上中心序列与下中心序列。本文的目的是推广这些结果在两个不同的方向，使用新的方法与非阿贝尔张量积。特别地，我们证明了一个关于有限生成群的Schur-Baer定理.然后，我们应用这些新得到的结果来描述的$k$ -幂零乘子，$k\geq 2$，和其他不变量的群体。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
