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/