Geodesic
On a consequence of the Krohn--Rhodes theorem
Diskretnaya Matematika, Tome 11 (1999) no. 4, pp. 101-109

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The Krohn–Rhodes theorem on the cascade connected automata was proved under the assumption that the basis contains special group automata. In this paper, we show that if the basis contains the constant automata, then this restriction can be omitted and for any simple group $G$ it is sufficient to take an arbitrary group automaton, whose group has $G$ as a divisor. 
@article{DM_1999_11_4_a8,
     author = {S. V. Aleshin},
     title = {On a consequence of the {Krohn--Rhodes} theorem},
     journal = {Diskretnaya Matematika},
     pages = {101--109},
     publisher = {mathdoc},
     volume = {11},
     number = {4},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1999_11_4_a8/}
}
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S. V. Aleshin. On a consequence of the Krohn--Rhodes theorem. Diskretnaya Matematika, Tome 11 (1999) no. 4, pp. 101-109. http://geodesic.mathdoc.fr/item/DM_1999_11_4_a8/