Journal Title/Source

Commentationes Mathematicae Universitatis Carolinae

Publication Date

2000

Volume

41

Page Numbers

371-375

Document Type

Journal Article

Department

Mathematics and Computer Science

Abstract

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 clases 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 under which general–not necessarily commutative–diassociative A-loops are, in fact, Moufang. Here, we finish part of the program by characterizing Moufang A-loops. We also investigate simple diassociative A-loops as well as a class of centrally nilpotent diassociative A-loops. These results, in toto, reveal the distinguished positions two familiar classes of diassociative A-loops–namely groups and commutative Moufang loops–play in the general theory.

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