On the notion of lower central series for loops
Group Theory
2007-05-23 v1
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.
Cite
@article{arxiv.math/0410515,
title = {On the notion of lower central series for loops},
author = {Jacob Mostovoy},
journal= {arXiv preprint arXiv:math/0410515},
year = {2007}
}
Comments
6 pages