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.