Nilpotency and dimension series for loops

2005/10/07 by Jacob Mostovoy, Mostovoy, J.
Engineering · Mathematics · #17D99 #20N05 #FOS: Mathematics #Group Theory (math.GR) #History and Theory of Mathematics #Mathematics and Applications #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.math/0510161

openalex publication_date 2005/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We take a step towards the development of a nilpotency theory for loops based on the commutator-associator filtration instead of the lower central series. This nilpotency theory shares many essential features with the associative case. In particular, we show that the isolator of the nth commutator-associator subloop coincides with the nth dimension subloop over a field of characteristic zero.

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