Moufang Loops that Share Associator and Three Quarters of Their Multiplication Tables
نویسندگان
چکیده
منابع مشابه
Moufang Loops That Share Associator and Three Quarters of Their Multiplication Tables
Certain two constructions, due to Drápal, produce a group by modifying exactly one quarter of the Cayley table of another group. We present these constructions in a compact way, and generalize them to Moufang loops, using loop extensions. Both constructions preserve associators, the associator subloop, and the nucleus. We conjecture that two Moufang 2-loops of finite order n with equivalent ass...
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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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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: Rocky Mountain Journal of Mathematics
سال: 2006
ISSN: 0035-7596
DOI: 10.1216/rmjm/1181069461