On the notion of lower central series for loops

2004/10/24 by Jacob Mostovoy, Mostovoy, Jacob
Engineering · Mathematics · #20N05 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Group Theory (math.GR) #History and Theory of Mathematics #Mathematics and Applications #math.GR #msc:20N05

paper · pdf · doi:10.48550/arxiv.math/0410515

6 pages

arxiv created 2004/10/24 · openalex publication_date 2004/10/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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