The commutative Moufang loops with minimum conditions for subloops I
نویسندگان
چکیده
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 characterized by different conditions of finiteness of its multiplicative groups. Mathematics subject classification: 20N05.
منابع مشابه
The 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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