Malcev algebras corresponding to smooth almost left automorphic Moufang loops
نویسندگان
چکیده
منابع مشابه
The Structure of Free Automorphic Moufang Loops
We describe the structure of a free loop of rank n in the variety of automorphic Moufang loops as a subdirect product of a free group and a free commutative Moufang loop, both of rank n. In particular, the variety of automorphic Moufang loops is the join of the variety of groups and the variety of commutative Moufang loops.
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It is known that Moufang loops are closely related to groups as they have many properties in common. For instance, they both have an inverse for each element and satisfy Lagrange’s theorem. In this paper, we study the properties of a class of Moufang loops which are not groups, but all their proper subloops and proper quotient loops are groups.
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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 ...
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ژورنال
عنوان ژورنال: Journal of Algebra and Its Applications
سال: 2018
ISSN: 0219-4988,1793-6829
DOI: 10.1142/s0219498818502328