English

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