Geodesic
Commutative Moufang Loops with Finite Conjugacy Classes of Subloops
Matematičeskie zametki, Tome 73 (2003) no. 2, pp. 269-280.

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It is proved that the following conditions are equivalent for an arbitrary commutative Moufang loop $Q$: 1) the loop $Q$ is finite over the center; 2) every subloop of $Q$ defines a finite conjugacy class of subloops; 3) every associative subloop of $Q$ defines a finite conjugacy class of subloops; 4) every infinite associative subloop of $Q$ defines a finite conjugacy class of subloops. 
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     author = {N. I. Sandu},
     title = {Commutative {Moufang} {Loops} with {Finite} {Conjugacy} {Classes} of {Subloops}},
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N. I. Sandu. Commutative Moufang Loops with Finite Conjugacy Classes of Subloops. Matematičeskie zametki, Tome 73 (2003) no. 2, pp. 269-280. http://geodesic.mathdoc.fr/item/MZM_2003_73_2_a11/

[1] Bruck R. H., A Survey of Binary Systems, Springer-Verlag, Berlin, 1958 | Zbl

[2] Smith J. D. H., “Commutative Moufang loops: the first 50 years”, Algebras, Groups, and Geom., 2:3 (1985), 209–234 | MR | Zbl

[3] Quasigroups and Loops: Theory and Applications, eds. Chein O., Pflugfelder H. O., Smith J. D. H., Helderman Verlag, Berlin, 1990

[4] Sandu N. I., “O tsentralno nilpotentnykh kommutativnykh lupakh Mufang”, Kvazigruppy i lupy, Sb., Shtiintsa, Kishinev, 1979, 145–155 | MR

[5] Fuks L., Beskonechnye abelevy gruppy, T. 1, Mir, M., 1974

[6] Sandu N. I., “Assotsiatorno nilpotentnye lupy”, Izv. AN MSSR. Ser. fiz.-tekh. i matem. nauk, 1978, no. 1, 28–33 | MR | Zbl