EMBEDDING OF ABSOLUTELY FREE GROUPS INTO GROUPS $B(m,n,1)$ - Atabekian, V. S.; Pahlevanian, A. S. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2023)
In this paper we prove that each countable absolutely free group can be isomorphic embedded into groups $B(m,n,1)$ for arbitrary $m≥ 2$ and odd $n≥ 665$ . 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 $4$.
Keywords: absolutely free group; non-amenable group; Tarski’s number