An ‘‘extra” law for characterizing Moufang loops
نویسندگان
چکیده
منابع مشابه
On Moufang A-loops
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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The main result of this paper is the determination of all nonassociative Moufang loops of orders *31. Combinatorial type methods are used to consider a number of cases which lead to the discovery of 13 loops of the type in question and prove that there can be no others. All of the loops found are isomorphic to all of their loop isotopes, are solvable, and satisfy both Lagrange's theorem and Syl...
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An extensive study of Moufang loops is given in [2].1 One defect of that study is that it assumes Moufang's associativity theorem [6], the only published proof of which involves a complicated induction. Using pseudo-automorphisms along with recent methods of Kleinfeld and the author [S], we shall give simple noninductive proofs of three associativity theorems, one of which (Theorem 5.1) general...
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Moufang loops are one of the best-known generalizations of groups. There is only one countable family of nonassociative finite simple Moufang loops, arising from the split octonion algebras. We prove that every member of this family is generated by three elements, using the classical results on generators of unimodular groups.
متن کاملHalf-isomorphisms of Moufang Loops
We prove that if the squaring map in the factor loop of a Moufang loop Q over its nucleus is surjective, then every half-isomorphism of Q onto a Moufang loop is either an isomorphism or an anti-isomorphism. This generalizes all earlier results in this vein.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1972
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1972-0292987-8