3-Abelian Groups and Commutative Moufang Loops
نویسندگان
چکیده
منابع مشابه
On 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...
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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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The structure of the commutative Moufang loops (CML) with minimum condition for subloops is examined. In particular it is proved that such a CML Q is a finite extension of a direct product of a finite number of the quasicyclic groups, lying in the centre of the CML Q. It is shown that the minimum conditions for subloops and for normal subloops are equivalent in a CML. Moreover, such CML also ch...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1984
ISSN: 0195-6698
DOI: 10.1016/s0195-6698(84)80002-5