Geodesic
The automaton permutation group $AS_n$ generated by elements of infinite order
Diskretnaya Matematika, Tome 9 (1997) no. 3, pp. 117-124.

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For an arbitrary integer $n\ge2$ we consider the group $AS_n$, constituted by boundedly determinate functions of one variable defined by means of initial automata with finite number of states on the Moore diagram, with input and output alphabets $E_n=\{0,1,\dots,n-1\}$, which at each state $q$ realize the output function $\psi(q,x)$ equal to some permutation $f_q(x)$ on the set $E_n$; $f_q(x)$ is an element of the complete symmetric group $S_n$. For $AS_n$ we give explicit generating system of elements of infinite order. 
@article{DM_1997_9_3_a9,
     author = {V. V. Makarov},
     title = {The automaton permutation group $AS_n$ generated by elements of infinite order},
     journal = {Diskretnaya Matematika},
     pages = {117--124},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1997_9_3_a9/}
}
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V. V. Makarov. The automaton permutation group $AS_n$ generated by elements of infinite order. Diskretnaya Matematika, Tome 9 (1997) no. 3, pp. 117-124. http://geodesic.mathdoc.fr/item/DM_1997_9_3_a9/