Geodesic
Defining relations and the word problem for free periodic groups of odd order
Izvestiya. Mathematics , Tome 2 (1968) no. 4, pp. 935-942.

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We prove that the free periodic group of odd order $n\geqslant4381$ with $m>1$ generators cannot be given by a finite number of defining relations. The word problem for these groups is solvable. 
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P. S. Novikov; S. I. Adian. Defining relations and the word problem for free periodic groups of odd order. Izvestiya. Mathematics , Tome 2 (1968) no. 4, pp. 935-942. http://geodesic.mathdoc.fr/item/IM2_1968_2_4_a13/

[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] Arshon S. E., “Dokazatelstvo suschestvovaniya $n$-znachnykh beskonechnykh asimmetrichnykh posledovatelnostei”, Matem. sb., 2(44) (1937), 769–779 | Zbl