EMBEDDING OF ABSOLUTELY FREE GROUPS INTO GROUPS $B(m,n,1)$

V. S. Atabekian; A. S. Pahlevanian

doi:10.46991/PYSU:A/2008.42.3.025

EMBEDDING OF ABSOLUTELY FREE GROUPS INTO GROUPS $B(m,n,1)$

Authors

V. S. Atabekian Chair of Algebra and Geometry, YSU, Armenia
A. S. Pahlevanian Chair of Algebra and Geometry, YSU, Armenia

DOI:

https://doi.org/10.46991/PYSU:A/2008.42.3.025

Keywords:

absolutely free group, non-amenable group, Tarski’s number

Abstract

In this paper we prove that each countable absolutely free group can be isomorphic embedded into groups $B(m,n,1)$ for arbitrary $m\geq 2$ and odd $n\geq 665$ . 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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Published

2023-10-06

How to Cite

Atabekian, V. S., & Pahlevanian, A. S. (2023). EMBEDDING OF ABSOLUTELY FREE GROUPS INTO GROUPS $B(m,n,1)$. Proceedings of the YSU A: Physical and Mathematical Sciences, 42(3 (217), 25–33. https://doi.org/10.46991/PYSU:A/2008.42.3.025