A Generalization of Moufang and Steiner Loops

2001/05/31 by Michael K. Kinyon, Kenneth Kunen, J. D. Phillips
Mathematics · #math.GR #msc:20N05

paper · pdf

published as Algebra Universalis 48 (2002), no. 1, 81--101 · 19 pp., 1 fig., uses amsart.cls, pifont.sty; to appear in Algebra Universalis

arxiv created 2001/11/22 · arxiv updated 2009/11/30

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.

Related

• Steiner Loops Satisfying the Statement of Moufang's Theorem
• Every diassociative A-loop is Moufang
• Moufang Theorem for a variety of local non-Moufang loops
• Semiautomorphic Inverse Property Loops
• Simple Moufang loops and Galois extensions