Geodesic
A lower bound for the growth of a 3-generator 2-group
Sbornik. Mathematics, Tome 192 (2001) no. 11, pp. 1661-1676 Cet article a éte moissonné depuis la source Math-Net.Ru

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A non-trivial lower bound is obtained for the growth of a certain periodic 3-generator group. It gives the negative answer to a conjecture of Grigorchuk posed in 1990. 
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Yu. G. Leonov. A lower bound for the growth of a 3-generator 2-group. Sbornik. Mathematics, Tome 192 (2001) no. 11, pp. 1661-1676. http://geodesic.mathdoc.fr/item/SM_2001_192_11_a3/

[1] Grigorchuk R. I., “K probleme Bernsaida o periodicheskikh gruppakh”, Funkts. analiz i ego prilozh., 14:1 (1980), 53–54 | MR | Zbl

[2] Grigorchuk R. I., “Primer konechno opredelennoi amenabelnoi gruppy, ne prinadlezhaschei klassu $EG$”, Matem. sb., 189:1 (1998), 79–100 | MR | Zbl

[3] de la Harpe P., Topics in geometric group theory, Preprint, http://www.unige.ch/math/biblio/preprint/pp98.html | MR | Zbl

[4] Milnor J., “Problem 5603”, Amer. Math. Monthly, 75:6 (1968), 685–686 | DOI | MR

[5] Grigorchuk R. I., “Stepeni rosta konechno porozhdennykh grupp i teoriya invariantnykh srednikh”, Izv. AN SSSR. Ser. matem., 48:5 (1984), 939–985 | MR

[6] Grigorchuk R. I., “O ryade Gilberta–Puankare graduirovannykh algebr, assotsiirovannykh s gruppami”, Matem. sb., 180:2 (1989), 207–225 | MR

[7] Klaas G., Leedham-Green C. R., Plesken W., Linear pro-$p$-groups of finite width, Lecture Notes in Math., 1674, Springer-Verlag, Berlin, 1997 | MR

[8] Bartholdi L., Grigorchuk R. I., “Lie methods in growth of groups and groups of finite width”, Computational and geometric aspects of modern algebra, Proceedings of the workshop (Edinburgh, UK, July 23–31, 1998), eds. M. Atkinson et al., Cambridge Univ. Press, Cambridge, 2000, 1–27 | MR | Zbl

[9] Grigorchuk R. I., “On growth in group theory”, Proceedings of the International Congress of Mathematicians, V. I (Kyoto, 1990), Math. Soc. Japan, Tokyo, 1991, 325–338 | MR | Zbl

[10] Leonov Yu. G., “On growth function for some torsion residually finite groups”, Pontrjagin Int. Math. Conf., Abstr. (Moscow), 1998, 36–38

[11] Rozhkov A. V., Usloviya konechnosti v gruppakh avtomorfizmov derevev, Dis. $\dots$ dokt. fiz.-matem. nauk, Chelyabinskii gos. un-t, 1996

[12] Leonov Yu. G., “Problema sopryazhennosti v odnom klasse $2$-grupp”, Matem. zametki, 64:4 (1998), 573–583 | MR | Zbl

[13] Bartholdi L., Lower bounds on the growth of Grigorchuk's torsion group, Preprint, 2000