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Research articles

The commutative Moufang loops with minimum conditions for subloops I

N. I. Sandu

State Agricultural University of Moldova, Chişinău, Moldova

Abstract: 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.

Keywords and phrases: Commutative Moufang loop, multiplicative group of loop, minimum condition for subloops, minimum condition for normal subloops.

MSC: 20N05

Received: 11.03.2003

Language: English

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