Commutative Moufang loops and distributive groupoids of small orders
نویسندگان
چکیده
منابع مشابه
On decomposition of commutative Moufang groupoids
X iv :0 80 3. 04 72 v1 [ m at h. R A ] 4 M ar 2 00 8 On decomposition of commutative Moufang groupoids B.V.Novikov It is well-known that the multiplicative groupoid of an alternative/Jordan algebra satisfies Moufang identities [1, 4]. Therefore it seems interesting to study the structure of such groupoids. In this note we apply to Moufang groupoids an approach which is widespread in Semigroup T...
متن کاملPossible 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.
متن کاملMoufang Loops of Small Order
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...
متن کاملOn Frattini subloops and normalizers of commutative Moufang loops
Let L be a commutative Moufang loop (CML) with multiplication group M, and let F(L), F(M) be the Frattini subgroup and Frattini subgroup of L and M respectively. It is proved that F(L) = L if and only if F(M) = M and is described the structure of this CLM. Constructively it is defined the notion of normalizer for subloops in CML. Using this it is proved that if F(L) 6= L then L satisfies the no...
متن کاملSelfdistributive Groupoids of Small Orders
After enumerating isomorphism types of at most five-element left distributive groupoids, we prove that a distributive groupoid with less than 81 elements is necessarily medial.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1981
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1981.101778