Geodesic
Embedding of absolutely free groups into groups $B(m,n,1)$
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2008), pp. 25-33.

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In this paper we prove that each countable absolutely free group can be isomorphic embedded into groups$B(m,n,1)$ for arbitrary $m \ge 2$ and odd $n \ge 665$. Thereby is shown that each group $B(m,n,1)$ generates the variety of all groups, and groups $B(m,n,1)$ are non-amenable. Particularly Tarski’s number is equal to $4$. 
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V. S. Atabekyan; A. S. Pahlevanyan. Embedding of absolutely free groups into groups $B(m,n,1)$. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2008), pp. 25-33. http://geodesic.mathdoc.fr/item/UZERU_2008_3_a3/

[1] J. Tits, “Free subgroups in linear groups”, J. Algebra, 20 (1972), 250–270 | DOI | MR | Zbl

[2] A. M. Vershik, “Komentarii k statyam Dzh. fon Neimana”, Dzh. fon Neiman Izbrannye trudy po funktsionalnom analizu, v. 1, 1987, 357–376 | MR

[3] J. von Neumann, “Zur allgemeinen Theorie des Masses”, Fundamenta Mathematicae, 13 (1929), 73–116 | Zbl

[4] R. I. Grigorchuk, “Symmetrical random walks on discrete groups”, Adv. Probab. Related Topics, v. 6, eds. R. L. Dobrushin, Ya. G. Sinai, 1980, 285–325 | MR | Zbl

[5] R. I. Grigorchuk, “An example of a finitely presented amenable group not belonging to the class $EG$”, Sb. Math., 189:1 (1998), 75–95 | DOI | DOI | MR | Zbl

[6] Ol'shanskii, Russian Math. Surveys, 35:4 (1980), 180–181 | DOI | MR | Zbl

[7] Math. USSR-Izv., 21:3 (1983), 425–434 | DOI | MR | Zbl | Zbl

[8] H. Kesten, “Symmetric random walks on groups”, Trans. Amer. Math. Soc., 92:2 pages 336–354 (1959) | DOI | MR | Zbl

[9] A. Yu. Ol’shanskii, M. V. Sapir, “Non-amenable finitely presented torsion-by-cyclic groups”, Publ. Math. Inst. Hautes Etudes Sci., 96 (2003), 43–169 | DOI | MR

[10] J.M. Cohen, “Cogrowth and amenability of discrete groups”, J. Funct. Anal., 48:3 (1982), 301–309 | DOI | MR | Zbl

[11] D.V. Osin, “Uniform non-amenability of free Burnside groups”, Arch. Math. (Basel), 88:5 (2007), 403–412 | DOI | MR | Zbl

[12] S. I. Adyan, Problema Bernsaida i tozhdestva v gruppakh, Nauka, M., 1975 | MR