Half-isomorphisms of Finite Automorphic Moufang Loops
نویسندگان
چکیده
منابع مشابه
Half-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.
متن کاملThe Structure of Free Automorphic Moufang Loops
We describe the structure of a free loop of rank n in the variety of automorphic Moufang loops as a subdirect product of a free group and a free commutative Moufang loop, both of rank n. In particular, the variety of automorphic Moufang loops is the join of the variety of groups and the variety of commutative Moufang loops.
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.
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The first class of nonassociative simple Moufang loops was discovered by L. Paige in 1956 [9], who investigated Zorn’s and Albert’s construction of simple alternative rings. M. Liebeck proved in 1987 [7] that there are no other finite nonassociative simple Moufang loops. We can briefly describe the class as follows: For every finite field F, there is exactly one simple Moufang loop. Recall Zorn...
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the textit{commutativity degree}, $pr(g)$, of a finite group $g$ (i.e. the probability that two (randomly chosen) elements of $g$ commute with respect to its operation)) has been studied well by many authors. it is well-known that the best upper bound for $pr(g)$ is $frac{5}{8}$ for a finite non--abelian group $g$. in this paper, we will define the same concept for a finite non--abelian textit{...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2016
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927872.2015.1087540