Nilpotency and dimension series for loops

Details Nilpotency and dimension series for loops Nilpotency and dimension series for loops

2005-10-07

arxiv.org/abs/math/0510161v1

Mathematics

Group Theory

10 pages, no figures

Scientific paper

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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