Geodesic
Profinite closures of the iterated monodromy groups associated with quadratic polynomials
Algebra and discrete mathematics, Tome 23 (2017) no. 2, pp. 285-304 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we describe the profinite closure of the iterated monodromy groups arising from the arbitrary post-critically finite quadratic polynomial.
Keywords: iterated monodromy groups, quadratic polynomials, profinite grous, profinite limits, group acting on trees. 
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     author = {Ihor Samoilovych},
     title = {Profinite closures of the iterated monodromy groups associated with quadratic polynomials},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2017_23_2_a10/}
}
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Ihor Samoilovych. Profinite closures of the iterated monodromy groups associated with quadratic polynomials. Algebra and discrete mathematics, Tome 23 (2017) no. 2, pp. 285-304. http://geodesic.mathdoc.fr/item/ADM_2017_23_2_a10/

[1] L. Bartholdi, V. V. Nekrashevych, “Iterated monodromy groups of quadratic polynomials, I”, Groups, Geometry, and Dynamics, 2:3 (2008), 309–336 | DOI | MR | Zbl

[2] A. M. Brunner, S. Sidki, “On the Automorphism Group of the One-Rooted Binary Tree”, Journal of Algebra, 195:2 (1997), 465–486 | DOI | MR | Zbl

[3] L. Bartholdi, B. Virág, “Amenability via random walks”, Duke Mathematical Journal, 130:1 (2005), 39–56 | DOI | MR | Zbl

[4] I. V. Bondarenko, I. O. Samoilovych, “On finite generation of self-similar groups of finite type”, International Journal of Algebra and Computation, 23:1 (2013), 69–79 | DOI | MR | Zbl

[5] R. I. Grigorchuk, A. Żuk, “On a torsion-free weakly branch group defined by a three state automaton”, International Journal of Algebra and Computation, 12:01n02 (2002), 223–246 | DOI | MR | Zbl

[6] V. Nekrashevych, Self-Similar Groups, Mathematical Surveys and Monographs, 117, American Mathematical Soc., 2005, 231 pp. | DOI | MR | Zbl

[7] R. Pink, Profinite iterated monodromy groups arising from quadratic polynomial, 2013, arXiv: 1307.5678

[8] Z. Šunić, “Hausdorff dimension in a family of self-similar groups”, Geometriae Dedicata, 124:1 (2007), 213–236 | DOI | MR