On the nuclei of Moufang loops with orders coprime to six
نویسندگان
چکیده
منابع مشابه
Possible orders of nonassociative Moufang loops
The paper surveys the known results concerning the question: “For what values of n does there exist a nonassociative Moufang loop of order n?” Proofs of the newest results for n odd, and a complete resolution of the case n even are also presented.
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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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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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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.
متن کاملMoufang Loops with Commuting Inner Mappings
We investigate the relation between the structure of a Moufang loop and its inner mapping group. Moufang loops of odd order with commuting inner mappings have nilpotency class at most two. 6-divisible Moufang loops with commuting inner mappings have nilpotency class at most two. There is a Moufang loop of order 2 with commuting inner mappings and of nilpotency class three.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2014
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2013.10.033