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. 
@article{MZM_2003_73_2_a11,
     author = {N. I. Sandu},
     title = {Commutative {Moufang} {Loops} with {Finite} {Conjugacy} {Classes} of {Subloops}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {269--280},
     publisher = {mathdoc},
     volume = {73},
     number = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_73_2_a11/}
}
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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/