Geodesic
Automaton representation of a free group
Diskretnaya Matematika, Tome 23 (2011) no. 3, pp. 32-56 
S. V. Aleshin. Automaton representation of a free group. Diskretnaya Matematika, Tome 23 (2011) no. 3, pp. 32-56. http://geodesic.mathdoc.fr/item/DM_2011_23_3_a2/
@article{DM_2011_23_3_a2,
     author = {S. V. Aleshin},
     title = {Automaton representation of a~free group},
     journal = {Diskretnaya Matematika},
     pages = {32--56},
     year = {2011},
     volume = {23},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2011_23_3_a2/}
}
TY  - JOUR
AU  - S. V. Aleshin
TI  - Automaton representation of a free group
JO  - Diskretnaya Matematika
PY  - 2011
SP  - 32
EP  - 56
VL  - 23
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/DM_2011_23_3_a2/
LA  - ru
ID  - DM_2011_23_3_a2
ER  - 
%0 Journal Article
%A S. V. Aleshin
%T Automaton representation of a free group
%J Diskretnaya Matematika
%D 2011
%P 32-56
%V 23
%N 3
%U http://geodesic.mathdoc.fr/item/DM_2011_23_3_a2/
%G ru
%F DM_2011_23_3_a2

Voir la notice de l'article provenant de la source Math-Net.Ru

We suggest a new example of a free subgroup of a group of automaton substitutions. We present two automata with three states which generate this subgroup; the inner semigroups of these automata are not groups.

[1] Kudryavtsev V. B., Aleshin S. V., Podkolzin A. S., Vvedenie v teoriyu avtomatov, Nauka, Moskva, 1985 | MR | Zbl

[2] Kargapolov M. I., Merzlyakov Yu. I., Osnovy teorii grupp, Nauka, Moskva, 1982 | MR | Zbl

[3] Aleshin S. A., “Svobodnaya gruppa konechnykh avtomatov”, Vestnik Moskovskogo univ., ser. I, 1983, no. 4, 12–14 | MR | Zbl

[4] Vorobets M., Vorobets Y., “On a free group of transformations defined by an automaton”, Geom. Dedicata, 124 (2007), 237–249 | DOI | MR | Zbl

[5] Żuk A., “Groupes engendrés par les automates”, Astérisque, 317 (2008), 141–174 | MR | Zbl

[6] Bondarenko I., Grigorchuk R., Kravchenko R., Muntyan Y., Nekrashevych V., Savchuk D., Šunić Z., “On classification of groups generated by 3-state automata over a 2-letter alphabet”, Algebra Discrete Math., 2008, no. 1, 1–163 | MR | Zbl