arXiv 0804.39562008-04-24math.RA

The commutative Moufang loops with minimum conditions for subloops I

N. I. Sandu

备注：: 18 pages
发表信息：: Buletinul Academiei de Stiinte a Republicii Moldova. Matematica, 2003, 3(43), pp. 25-40

英文摘要：

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 multiplication groups.

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