$F$-quasigroups isotopic to Moufang loops
نویسندگان
چکیده
منابع مشابه
F-quasigroups Isotopic to Groups
In [5] we showed that every loop isotopic to an F-quasigroup is a Moufang loop. Here we characterize, via two simple identities, the class of F-quasigroups which are isotopic to groups. We call these quasigroups FGquasigroups. We show that FG-quasigroups are linear over groups. We then use this fact to describe their structure. This gives us, for instance, a complete description of the simple F...
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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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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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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1979
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1979.101579