Geodesic
On free semigroups of automaton transformations
Matematičeskie zametki, Tome 63 (1998) no. 2, pp. 248-259

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It is established that the subset of free $k$-generated subsemigroups of the semigroup of all automaton transformations over a finite alphabet is a second category set (in the sense of the Baire category approach) in the set of all $k$-generated subsemigroups. A continuum series of pairs of automaton transformations each of which generates a free semigroup of rank two is indicated. A criterion is established for this semigroup to be a finite-automaton group. 
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     author = {A. S. Oliinyk},
     title = {On free semigroups of automaton transformations},
     journal = {Matemati\v{c}eskie zametki},
     pages = {248--259},
     publisher = {mathdoc},
     volume = {63},
     number = {2},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_63_2_a8/}
}
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A. S. Oliinyk. On free semigroups of automaton transformations. Matematičeskie zametki, Tome 63 (1998) no. 2, pp. 248-259. http://geodesic.mathdoc.fr/item/MZM_1998_63_2_a8/