automgrp : a GAP 4 package - References

defcprime′

[AKL]

Ali Akhavi, Ines Klimann, Sylvain Lombardy, Jean Mairesse, and Matthieu Picantin.
On the finiteness problem for automaton (semi)groups.
Internat. J. Algebra Comput., 22(6):1250052, 26, 2012.

[Ale83]

S. V. Aleshin.
A free group of finite automata.
Vestnik Moskov. Univ. Ser. I Mat. Mekh., (4):12--14, 1983.

[Bar03]

Laurent Bartholdi.
A Wilson group of non-uniformly exponential growth.
C. R. Math. Acad. Sci. Paris, 336(7):549--554, 2003.

[BG02]

Laurent Bartholdi and Rostislav I. Grigorchuk.
On parabolic subgroups and Hecke algebras of some fractal groups.
Serdica Math. J., 28(1):47--90, 2002.

[BGK32]

I. Bondarenko, R. Grigorchuk, R. Kravchenko, Y. Muntyan, V. Nekrashevych, D. Savchuk, and Z. \vSunić.
Classification of groups generated by 3-state automata over 2-letter alphabet.
Algebra Discrete Math., (1):1--163, 2008.

[BGK07]

I. Bondarenko, R. Grigorchuk, R. Kravchenko, Y. Muntyan, V. Nekrashevych, D. Savchuk, and Z. \vSunić.
Groups generated by 3-state automata over a 2-letter alphabet. II.
J. Math. Sci. (N. Y.), 156(1):187--208, 2009.
Functional analysis.

[BKNV05]

Laurent Bartholdi, Vadim Kaimanovich, and Volodymyr Nekrashevych.
On amenability of automata groups.
Duke Mathematical Journal, 154(3):575--598, 2010.

[BN06]

Laurent I. Bartholdi and Volodymyr V. Nekrashevych.
Thurston equivalence of topological polynomials.
Acta Math., 197(1):1--51, 2006.

[BP06]

Kai-Uwe Bux and Rodrigo Pérez.
On the growth of iterated monodromy groups.
In Topological and asymptotic aspects of group theory, volume 394 of Contemp. Math., pages 61--76. Amer. Math. Soc., Providence, RI, 2006.
(available at http://www.arxiv.org/abs/math.GR/0405456).

[BRS06]

L. Bartholdi, I. I. Reznykov, and V. I. Sushchansky.
The smallest Mealy automaton of intermediate growth.
J. Algebra, 295(2):387--414, 2006.

[BS07]

Ievgen V. Bondarenko and Dmytro M. Savchuk.
On Sushchansky p-groups.
Algebra Discrete Math., (2):22--42, 2007.

[BV05]

Laurent Bartholdi and Bálint Virág.
Amenability via random walks.
Duke Math. J., 130(1):39--56, 2005.
(available at http://arxiv.org/abs/math.GR/0305262).

[Ers04]

Anna Erschler.
Boundary behavior for groups of subexponential growth.
Annals of Math., 160(3):1183--1210, 2004.

[FG85]

Jacek Fabrykowski and Narain Gupta.
On groups with sub-exponential growth functions.
J. Indian Math. Soc. (N.S.), 49(3-4):249--256 (1987), 1985.

[GLSZ00]

Rostislav I. Grigorchuk, Peter Linnell, Thomas Schick, and Andrzej Zuk.
On a question of Atiyah.
C. R. Acad. Sci. Paris Sér. I Math., 331(9):663--668, 2000.

[GNS00]

R. I. Grigorchuk, V. V. Nekrashevich, and V. I. Sushchanski\ui.
Automata, dynamical systems, and groups.
Tr. Mat. Inst. Steklova, 231(Din. Sist., Avtom. i Beskon. Gruppy):134--214, 2000.

[Gri80]

R. I. Grigor\vcuk.
On Burnside's problem on periodic groups.
Funktsional. Anal. i Prilozhen., 14(1):53--54, 1980.

[Gri84]

R. I. Grigorchuk.
Degrees of growth of finitely generated groups and the theory of invariant means.
Izv. Akad. Nauk SSSR Ser. Mat., 48(5):939--985, 1984.

[Gri05]

Rostislav Grigorchuk.
Solved and unsolved problems around one group.
In Infinite groups: geometric, combinatorial and dynamical aspects, volume 248 of Progr. Math., pages 117--218. Birkh"auser, Basel, 2005.

[GS83]

Narain Gupta and Sa"id Sidki.
On the Burnside problem for periodic groups.
Math. Z., 182(3):385--388, 1983.

[GS06a]

Rostislav Grigorchuk and Zoran \vSuni&kacute;.
Asymptotic aspects of Schreier graphs and Hanoi Towers groups.
C. R. Math. Acad. Sci. Paris, 342(8):545--550, 2006.

[GS06b]

Rostislav Grigorchuk and Zoran \vSunić.
Schreier spectrum of the Hanoi Towers group on three pegs.
In Analysis on graphs and its applications, volume 77 of Proc. Sympos. Pure Math., pages 183--198. Amer. Math. Soc., Providence, RI, 2008.

[GSESS]

Rostislav Grigorchuk and Dmytro Savchuk.
Self-similar groups acting essentially freely on the boundary of the binary rooted tree.
In Group Theory, Combinatorics, and Computing, volume 611 of Contemp. Math. Amer. Math. Soc., Providence, RI, 2014.

[GSS07]

Rostislav Grigorchuk, Dmytro Savchuk, and Zoran \vSunić.
The spectral problem, substitutions and iterated monodromy.
CRM Proceedings and Lecture Notes, 42(8):225--248, 2007.

[GZ02a]

Rostislav I. Grigorchuk and Andrzej Zuk.
On a torsion-free weakly branch group defined by a three state automaton.
Internat. J. Algebra Comput., 12(1-2):223--246, 2002.

[GZ02b]

Rostislav I. Grigorchuk and Andrzej Zuk.
Spectral properties of a torsion-free weakly branch group defined by a three state automaton.
In Computational and statistical group theory (Las Vegas, NV/Hoboken, NJ, 2001), volume 298 of Contemp. Math., pages 57--82. Amer. Math. Soc., Providence, RI, 2002.

[KLI]

Ines Klimann.
The finiteness of a group generated by a 2-letter invertible-reversible Mealy automaton is decidable.
In Natacha Portier and Thomas Wilke, editors, 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013), volume 20 of Leibniz International Proceedings in Informatics (LIPIcs), pages 502--513, Dagstuhl, Germany, 2013. Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik.

[Nek07]

Volodymyr Nekrashevych.
A minimal Cantor set in the space of 3-generated groups.
Geom. Dedicata, 124:153--190, 2007.

[Sid00]

Said Sidki.
Automorphisms of one-rooted trees: growth, circuit structure, and acyclicity.
J. Math. Sci. (New York), 100(1):1925--1943, 2000.

[Sus79]

V. I. Sushchansky.
Periodic permutation p-groups and the unrestricted Burnside problem.
DAN SSSR., 247(3):557--562, 1979.
(in Russian).

[VV05]

Mariya Vorobets and Yaroslav Vorobets.
On a free group of transformations defined by an automaton.
Geom. Dedicata, 124:237--249, 2007.

[Wil04]

John S. Wilson.
On exponential growth and uniformly exponential growth for groups.
Invent. Math., 155(2):287--303, 2004.

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