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Displaying similar documents to “Moufang trees and generalized quadrangles.”

On Moufang A-loops

Jon D. Phillips (2000)

Commentationes Mathematicae Universitatis Carolinae

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In a series of papers from the 1940’s and 1950’s, R.H. Bruck and L.J. Paige developed a provocative line of research detailing the similarities between two important classes of loops: the diassociative A-loops and the Moufang loops ([1]). Though they did not publish any classification theorems, in 1958, Bruck’s colleague, J.M. Osborn, managed to show that diassociative, commutative A-loops are Moufang ([5]). In [2] we relaunched this now over 50 year old program by examining conditions...

Moufang loops of order 243

Michael C. Slattery, Ashley L. Zenisek (2012)

Commentationes Mathematicae Universitatis Carolinae

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We present a computer-assisted determination of the 72 non-isomorphic, non-associative Moufang loops of order 243. Some of their properties and distinguishing features are discussed.

The commingling of commutativity and associativity in Bol loops

Jon D. Phillips (2016)

Commentationes Mathematicae Universitatis Carolinae

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Commutative Moufang loops were amongst the first (nonassociative) loops to be investigated; a great deal is known about their structure. More generally, the interplay of commutativity and associativity in (not necessarily commutative) Moufang loops is well known, e.g., the many associator identities and inner mapping identities involving commutant elements, especially those involving the exponent three. Here, we investigate all of this in the variety of Bol loops.