Unrestricted wreath products and sofic groups
Group Theory
2018-02-14 v1
Abstract
We show that the unrestricted wreath product of a sofic group by an amenable group is sofic. We use this result to present an alternative proof of the known fact that any group extension with sofic kernel and amenable quotient is again a sofic group. Our approach exploits the famous Kaloujnine-Krasner theorem and extends, with an additional argument, to hyperlinear-by-amenable groups.
Keywords
Cite
@article{arxiv.1802.04688,
title = {Unrestricted wreath products and sofic groups},
author = {Goulnara Arzhantseva and Federico Berlai and Martin Finn-Sell and Lev Glebsky},
journal= {arXiv preprint arXiv:1802.04688},
year = {2018}
}
Comments
10 pages