A Generalization of Moufang and Steiner Loops

Abstract

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.

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