On torsion-free nilpotent loops
Group Theory
2016-10-24 v1
Abstract
We show that a torsion-free nilpotent loop (that is, a loop nilpotent with respect to the dimension filtration) has a torsion-free nilpotent left multiplication group of, at most, the same class. We also prove that a free loop is residually torsion-free nilpotent and that the same holds for any free commutative loop. Although this last result is much stronger than the usual residual nilpotency of the free loop proved by Higman, it is proved, essentially, by the same method.
Keywords
Cite
@article{arxiv.1610.06663,
title = {On torsion-free nilpotent loops},
author = {J. Mostovoy and J. M. Perez-Izquierdo and I. P. Shestakov},
journal= {arXiv preprint arXiv:1610.06663},
year = {2016}
}