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.

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. 
@article{BASM_2003_3_a2,
     author = {N. I. Sandu},
     title = {The commutative {Moufang} loops with minimum conditions for {subloops~I}},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {25--40},
     publisher = {mathdoc},
     number = {3},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2003_3_a2/}
}
TY  - JOUR
AU  - N. I. Sandu
TI  - The commutative Moufang loops with minimum conditions for subloops~I
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2003
SP  - 25
EP  - 40
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BASM_2003_3_a2/
LA  - en
ID  - BASM_2003_3_a2
ER  - 
%0 Journal Article
%A N. I. Sandu
%T The commutative Moufang loops with minimum conditions for subloops~I
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2003
%P 25-40
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BASM_2003_3_a2/
%G en
%F BASM_2003_3_a2
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/

[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