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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     author = {O. A. Sarkisyan},
     title = {On~the word and divisibility problems in semigroups and groups without cycles},
     journal = {Izvestiya. Mathematics },
     pages = {643--656},
     publisher = {mathdoc},
     volume = {19},
     number = {3},
     year = {1982},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1982_19_3_a6/}
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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/