Geodesic
On abelian subgroups and the conjugacy problem in free periodic
Izvestiya. Mathematics , Tome 2 (1968) no. 5, pp. 1131-1144.

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We prove the finiteness of any abelian subgroup of a free periodic group of odd order $n \geqslant4381$. We also show that for these groups the conjugacy problem is solvable. 
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P. S. Novikov; S. I. Adian. On abelian subgroups and the conjugacy problem in free periodic. Izvestiya. Mathematics , Tome 2 (1968) no. 5, pp. 1131-1144. http://geodesic.mathdoc.fr/item/IM2_1968_2_5_a11/

[1] Novikov P. S., Adyan S. I., “O beskonechnykh periodicheskikh gruppakh. I, II, III”, Izv. AN SSSR. Ser. matem., 32:1 (1968), 212–244 ; 2, 251–524 ; 3, 709–731 | MR | Zbl | MR | MR

[2] Novikov P. S., Adyan S. I., “Opredelyayuschie sootnosheniya i problema tozhdestva dlya svobodnykh periodicheskikh grupp nechetnogo poryadka”, Izv. AN SSSR. Ser. matem., 32 (1968), 971–979 | Zbl