A Generalization of Moufang and Steiner Loops

Details A Generalization of Moufang and Steiner Loops A Generalization of Moufang and Steiner Loops

2001-05-02

arxiv.org/abs/math/0105015v2

Algebra Universalis 48 (2002), no. 1, 81--101

Mathematics

Group Theory

19 pp., 1 fig., uses amsart.cls, pifont.sty; to appear in Algebra Universalis

Scientific paper

We study a variety of loops, RIF, which arise naturally from considering
inner mapping groups, and a somewhat larger variety, ARIF. All Steiner and
Moufang loops are RIF, and all flexible C-loops are ARIF. We show that all ARIF
loops are diassociative, thus generalizing Moufang's Theorem.

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