Examples of Finitely Generated Metabelian Groups Not Residually Finite with Respect to Conjugacy and Occurrence, and Representation of Groups of the Form

We give two examples of finitely generated metabelian groups which concern problems of residual finiteness: In the first example, the group is not residually finite with respect to conjugacy, while in the second, we prove that the Baumslag–Solitar group  , with  a prime, is not residually finite wit...

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Bibliographic Details
Published in:Siberian mathematical journal 2023, Vol.64 (3), p.686-690
Main Author: Timoshenko, E. I.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Representations
Subgroups
Online Access:Get full text
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Summary:We give two examples of finitely generated metabelian groups which concern problems of residual finiteness: In the first example, the group is not residually finite with respect to conjugacy, while in the second, we prove that the Baumslag–Solitar group  , with  a prime, is not residually finite with respect to occurrence in cyclic subgroups. Also, we find some representation of the quotient group of the form .
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446623030151