Geodesic
On $F$-semigroups with three generators
Matematičeskie zametki, Tome 14 (1973) no. 2, pp. 267-277 
L. G. Budkina; A. A. Markov. On $F$-semigroups with three generators. Matematičeskie zametki, Tome 14 (1973) no. 2, pp. 267-277. http://geodesic.mathdoc.fr/item/MZM_1973_14_2_a12/
@article{MZM_1973_14_2_a12,
     author = {L. G. Budkina and A. A. Markov},
     title = {On $F$-semigroups with three generators},
     journal = {Matemati\v{c}eskie zametki},
     pages = {267--277},
     year = {1973},
     volume = {14},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_2_a12/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

All $F$-semigroups (i.e., semigroups isomorphic to finitely generated subsemigroups of a free semigroup) with three generators are finitely defined. The necessary and sufficient condition is obtained for which the equation in the words $Z^n=\varphi(X,Y)$ has a nontrival solution.