منابع مشابه
Random Generators of Given Orders and the Smallest Simple Moufang Loop
The probability that m randomly chosen elements of a finite power associative loop C have prescribed orders and generate C is calculated in terms of certain constants Γ related to the action of Aut(C) on the subloop lattice of C. As an illustration, all meaningful probabilities of random generation by elements of given orders are found for the smallest nonassociative simple Moufang loop. 1. Ran...
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Finite simple, unipotent Bol loops have recently been identified and constructed using group theory. However, the purely group-theoretical constructions of the actual loops are indirect, somewhat arbitrary in places, and rely on computer calculations to a certain extent. In the spirit of revisionism, this paper is intended to give a more explicit combinatorial specification of the smallest simp...
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An A-loop is a loop in which every inner mapping is an automorphism. A problem which had been open since 1956 is settled by showing that every diassociative A-loop is Moufang.
متن کاملGenerators for Finite Simple Moufang Loops
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 کاملCoverings of the smallest Paige loop
By investigating the construction of the split Cayley generalized hexagon, H(2), we get that there do not exist five distinct hexagon lines each a distance two apart from each other. From this we prove that the smallest Paige loop has a covering number of seven and that its automorphism group permutes these coverings transitively.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2008
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2007.03.049