Geodesic
The commutative Moufang loops with minimum conditions for subloops I
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2003), pp. 25-40 
N. I. Sandu. The commutative Moufang loops with minimum conditions for subloops I. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2003), pp. 25-40. http://geodesic.mathdoc.fr/item/BASM_2003_3_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Sandu N. I., “On locally normal loops”, Scripta scientiarum mathematicarum, 1:2 (1999), 364–380 | Zbl

[2] Sandu N. I., “Commutative Moufang loops with finite classes of conjugate elements”, Scripta scientiarum mathematicarum, 1:2 (1999), 381–394 | Zbl

[3] Sandu N. I., “Commutative Moufang loops with finite classes of conjugate subloops”, Mat. zametki, 73:2 (2003), 269–280 (In Russian) | MR | Zbl

[4] Bruck R. H., A survey of binary systems, Springer Verlag, Berlin–Heidelberg, 1958 | MR | Zbl

[5] Sandu N. I., “Centrally nilpotent commutative Moufang loops”, Quasigroups and loops, Mat. issled., 51, 1979, 145–155 (In Russian) | MR | Zbl

[6] Fuchs L., Infinite abelian groups, vol. 1, Mir, Moscow, 1974 (In Russian) | MR | Zbl

[7] Chernikov S. N., The groups with given properties of the systems of subgroups, Nauka, Moscow, 1980 (In Russian) | MR

[8] Zaitzev D. I., “Steadily solvable and steadily nilpotent groups”, DAN SSSR, 176:3 (1967), 509–511 (In Russian) | MR