关于循环的下中心序列概念
On the notion of lower central series for loops
摘要：
换位子演算是群论的基本工具之一。然而，它的扩展到非联想的情况下，基于通常的定义的下中心序列的循环，是不完全令人满意的。也就是说，与循环的下中心序列相关联的分次阿贝尔群不具有任何有趣的代数结构。在这篇文章中，我们构造了一个新的推广的下中心序列任意循环，是定制的，以产生一组多线性操作相关的分次群。
英文摘要：
The commutator calculus is one of the basic tools in group theory. However, its extension to the non-associative context, based on the usual definition of the lower central series of a loop, is not entirely satisfactory. Namely, the graded abelian group associated to the lower central series of a loop is not known to carry any interesting algebraic structure. In this note we construct a new generalization of the lower central series to arbitrary loops that is tailored to produce a set of multilinear operations on the associated graded group.
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。
