THE SET OF 2-GENERETED C∗ -SIMPLE RELATIVELY FREE GROUPS HAS THE CARDINALITY OF THE CONTINUUM

Varujan Atabekyan

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This work is licensed under Creative Commons Attribution–NonCommercial International License (CC BY-NC 4.0).

Abstract

In this paper we prove that the set of non-isomorphic 2-generated C∗-simple relatively free groups has the cardinality of the continuum. A non-trivial identity is satisfied in any (not absolutely free) relatively free group. Hence, they cannot contain a non-abelian absolutely free subgroups. The question of the existence of C∗-simple groups without free subgroups of rank 2 was posed by de la Harpe in 2007.

Author(s)

Table of Contents

THE SET OF 2-GENERETED C∗ -SIMPLE RELATIVELY FREE GROUPS HAS THE CARDINALITY OF THE CONTINUUM

Abstract

Author(s)

Table of Contents

Related Articles

ON UNIQUENESS OF HOLOMORPHIC AND BOUNDED OUTSIDE THE CLOSED LOGARITHMIC SECTOR FUNCTIONS REPRESENTABLE BY LACUNARY POWER SERIES

COMPUTER DETECTING AND PROCESSING OF THE SIGNALS OF A FLAT-COIL ABSOLUTE-POSITION SENSOR BASED SEISMIC DETECTOR

THE SET OF 2-GENERETED C∗ -SIMPLE RELATIVELY FREE GROUPS HAS THE CARDINALITY OF THE CONTINUUM

Abstract

Subscribe to TheGufo Newsletter​

Subscribe to TheGufo Newsletter