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...
متن کاملThe commutative Moufang loops with minimum conditions for subloops I
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...
متن کاملThe commutative Moufang loops with maximum conditions for subloops
It is proved that the maximum condition for subloops in a commutative Moufang loop Q is equivalent with the conditions of finite generating of different subloops of the loop Q and different subgroups of the multiplication group of the loop Q. An analogue equivalence is set for the commutative Moufang ZA-loops. Classification: 20N05
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For each proper divisor d of (q − √q + 1), q being a square power of a prime, maximal curves Fq-covered by the Hermitian curve of genus 1 2 ( q− √ q+1 d − 1) are constructed.
متن کاملOn Edge-Colored Graphs Covered by Properly Colored Cycles
We characterize edge-colored graphs in which every edge belongs to some properly colored cycle. We obtain our result by applying a characterization of 1-extendable graphs.
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ژورنال
عنوان ژورنال: Expositiones Mathematicae
سال: 2005
ISSN: 0723-0869
DOI: 10.1016/j.exmath.2005.01.009