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Nilpotency and dimension series for loops

J. Mostovoy
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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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J. Mostovoy. 2005-10-07. Nilpotency and dimension series for loops. https://arxiv.org/abs/math/0510161

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