English

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

R2 v1 2026-06-23T00:21:04.330Z