Research articles

Free Moufang loops and alternative algebras

N. I. Sandu

Tiraspol State University, Chisinau, Moldova

Abstract: It is proved that any free Moufang loop can be embedded in to a loop of invertible elements of some alternative algebra. Using this embedding it is quite simple to prove the well-known result: if three elements of Moufang loop are bound by the associative law, then they generate an associative subloop. It is also proved that the intersection of the terms of the lower central series of a free Moufang loop is the identity and that a finitely generated free Moufang loop is Hopfian.

Keywords and phrases: Moufang loop, lower central series, Hopfian loop, alternative algebra.

MSC: 17D05, 20N05

Received: 27.02.2008

Language: English

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