On approximation properties of semidirect products of groups
Group Theory
2020-08-28 v2 Dynamical Systems
Abstract
Let R be a class of groups closed under taking semidirect products with finite kernel and fully residually R-groups. We prove that R contains all R-by-{finitely generated residually finite} groups. It follows that a semidirect product of a finitely generated residually finite group with a surjunctive group is surjunctive. This remained unknown even for direct products of a surjunctive group with the integers Z.
Keywords
Cite
@article{arxiv.1312.7682,
title = {On approximation properties of semidirect products of groups},
author = {Goulnara Arzhantseva and Światosław R. Gal},
journal= {arXiv preprint arXiv:1312.7682},
year = {2020}
}
Comments
6 pages, no figures