Geodesic
On~the word and divisibility problems in semigroups and groups without cycles
Izvestiya. Mathematics , Tome 19 (1982) no. 3, pp. 643-656.

Voir la notice de l'article provenant de la source Math-Net.Ru

The author proves the solvability of the right and left divisibility problems, and consequently the word problem in semigroups with a system of defining relations that do not contain cycles. In particular the solvability of the word problem in groups without cycles is proved. Bibliography: 3 titles. 
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O. A. Sarkisyan. On~the word and divisibility problems in semigroups and groups without cycles. Izvestiya. Mathematics , Tome 19 (1982) no. 3, pp. 643-656. http://geodesic.mathdoc.fr/item/IM2_1982_19_3_a6/

[1] Adyan S. I., Opredelyayuschie sootnosheniya i algoritmicheskie problemy dlya grupp i polugrupp, Trudy Matem. in-ta im. V. A. Steklova AN SSSR, 85, 1966 | Zbl

[2] Adyan S. I., “O preobrazovaniyakh slov v polugruppe, zadannoi sistemoi opredelyayuschikh sootnoshenii”, Algebra i logika, 15:6 (1976), 611–621 | MR | Zbl

[3] Sarkisyan O. A., “Nekotorye sootnosheniya mezhdu problemami tozhdestva i delimosti v gruppakh i polugruppakh”, Izv. AN SSSR. Ser. matem., 43:4 (1979), 909–920 | MR