Geodesic
Functional equations in the theory of semigroups
Matematičeskie zametki, Tome 7 (1970) no. 5, pp. 635-640 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is established that the collection of regular solutions of the equation $f(t+s)=G[f(t),f(s)]$, where $G(\alpha, \beta)$ is a symmetric polynomial, coincides with the collection of semigroups. 
@article{MZM_1970_7_5_a11,
     author = {V. P. Anosov and P. E. Sobolevskii},
     title = {Functional equations in the theory of semigroups},
     journal = {Matemati\v{c}eskie zametki},
     pages = {635--640},
     year = {1970},
     volume = {7},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_7_5_a11/}
}
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V. P. Anosov; P. E. Sobolevskii. Functional equations in the theory of semigroups. Matematičeskie zametki, Tome 7 (1970) no. 5, pp. 635-640. http://geodesic.mathdoc.fr/item/MZM_1970_7_5_a11/