The commutative Moufang loops with minimum conditions for subloops I

Details The commutative Moufang loops with minimum conditions for subloops I The commutative Moufang loops with minimum conditions for subloops I

2008-04-24

arxiv.org/abs/0804.3956v1

Buletinul Academiei de Stiinte a Republicii Moldova. Matematica, 2003, 3(43), pp. 25-40

Mathematics

Rings and Algebras

18 pages

Scientific paper

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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