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On the notion of lower central series for loops

Jacob Mostovoy
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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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Jacob Mostovoy. 2004-10-24. On the notion of lower central series for loops. https://arxiv.org/abs/math/0410515

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