Geodesic
Uncountably many $2$-generated just-infinite branch pro-2 groups
Algebra and discrete mathematics, Tome 19 (2015) no. 1, pp. 8-18.

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

The aim of this note is to prove that there are $2^{\aleph_0}$ non-isomorphic 2 generated just-infinite branch pro-2 groups. 
@article{ADM_2015_19_1_a2,
     author = {Mustafa G\"okhan Benli and Rostislav Grigorchuk},
     title = {Uncountably many $2$-generated just-infinite branch pro-2 groups},
     journal = {Algebra and discrete mathematics},
     pages = {8--18},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2015_19_1_a2/}
}
TY  - JOUR
AU  - Mustafa Gökhan Benli
AU  - Rostislav Grigorchuk
TI  - Uncountably many $2$-generated just-infinite branch pro-2 groups
JO  - Algebra and discrete mathematics
PY  - 2015
SP  - 8
EP  - 18
VL  - 19
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2015_19_1_a2/
LA  - en
ID  - ADM_2015_19_1_a2
ER  - 
%0 Journal Article
%A Mustafa Gökhan Benli
%A Rostislav Grigorchuk
%T Uncountably many $2$-generated just-infinite branch pro-2 groups
%J Algebra and discrete mathematics
%D 2015
%P 8-18
%V 19
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2015_19_1_a2/
%G en
%F ADM_2015_19_1_a2
Mustafa Gökhan Benli; Rostislav Grigorchuk. Uncountably many $2$-generated just-infinite branch pro-2 groups. Algebra and discrete mathematics, Tome 19 (2015) no. 1, pp. 8-18. http://geodesic.mathdoc.fr/item/ADM_2015_19_1_a2/

[1] Mustafa Gökhan Benli, “Profinite completion of {G}rigorchuk's group is not finitely presented”, Internat. J. Algebra Comput., 22:5 (2012), 1250045, 26 pp. | DOI | MR | Zbl

[2] M. G. Benli, R. Grigorchuk, and T. Nagnibeda, Universal groups of intermediate growth and their invariant random subgroups, 2015, arXiv: http://arxiv.org/abs/1503.01705 | MR

[3] Pierre de la Harpe, Topics in geometric group theory, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 2000 | MR | Zbl

[4] R. I. Grigorchuk, W. N. Herfort, and P. A. Zalesskii, “The profinite completion of certain torsion $p$-groups”, Algebra (Moscow 1998), de Gruyter, Berlin, 2000, 113–123 | MR | Zbl

[5] R. I. Grigorchuk, “Degrees of growth of finitely generated groups and the theory of invariant means”, Izv. Akad. Nauk SSSR Ser. Mat., 48:5 (1984), 939–985 | MR

[6] R. I. Grigorchuk, “Degrees of growth of $p$-groups and torsion-free groups”, Mat. Sb. (N. S.), 126(168):2 (1985), 194–214 | MR | Zbl

[7] R. I. Grigorchuk, “Just infinite branch groups”, New horizons in pro-$p$ groups, Progr. Math., 184, Birkhäuser Boston, Boston, MA, 2000, 121–179 | MR | Zbl

[8] Snopce Ilir, Uncountably many non-commensurable finitely presented pro-$p$ groups, 2015, arXiv: http://arxiv.org/abs/1504.00027 | MR

[9] Yaroslav Lavreniuk and Volodymyr Nekrashevych, “Rigidity of branch groups acting on rooted trees”, Geom. Dedicata, 89 (2002), 159–179 | MR | Zbl

[10] Volodymyr Nekrashevych, “Self-similar groups”, Mathematical Surveys and Monographs, 117, American Mathematical Society, Providence, RI, 2005 | MR

[11] B. H. Neumann, “Some remarks on infinitem groups”, London. Math. Soc., 12 (1937), 120–127

[12] Nikolay Nikolov and Dan Segal, “On finitely generated profinite groups. I. Strong completeness and uniform bounds”, Ann. of Math. (2), 165:1 (2007), 171–238 | DOI | MR | Zbl

[13] E. L. Pervova, “Everywhere dense subgroups of a group of tree automorphisms”, Tr. Mat. Inst. Steklova, 231, Din. Sist., Avtom. i Beskon. Gruppy, 2000, 356–367 | MR | Zbl

[14] E. L. Pervova, Profinite topologies in just infinite branch groups, preprint 2002-154, Max Planck Institute for Mathematics, Bonn, Germany, 2002

[15] Luis Ribes and Pavel Zalesskii, Profinite groups, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. / A Series of Modern Surveys in Mathematics \newblock Springer-Verlag, Berlin, 40, second edition, 2010 | MR | Zbl

[16] John S. Wilson, “On just infinite abstract and profinite groups”, New horizons in pro-$p$ groups, Progr. Math., 184, Birkhäuser Boston, Boston, MA, 2000, 181–203 | MR | Zbl