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

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

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 $4$.
@article{UZERU_2008_3_a3,
     author = {V. S. Atabekyan and A. S. Pahlevanyan},
     title = {Embedding of absolutely free groups into groups $B(m,n,1)$},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {25--33},
     publisher = {mathdoc},
     number = {3},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZERU_2008_3_a3/}
}
TY  - JOUR
AU  - V. S. Atabekyan
AU  - A. S. Pahlevanyan
TI  - Embedding of absolutely free groups into groups $B(m,n,1)$
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 2008
SP  - 25
EP  - 33
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UZERU_2008_3_a3/
LA  - ru
ID  - UZERU_2008_3_a3
ER  - 
%0 Journal Article
%A V. S. Atabekyan
%A A. S. Pahlevanyan
%T Embedding of absolutely free groups into groups $B(m,n,1)$
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 2008
%P 25-33
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UZERU_2008_3_a3/
%G ru
%F UZERU_2008_3_a3
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/