A Generalization of Moufang and Steiner Loops
classification
🧮 math.GR
keywords
loopsarifmoufangsteinervarietyarisec-loopsconsidering
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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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