The Wreath Product of Two Sofic Groups is Sofic

TL;DR

This paper demonstrates that the wreath product of two sofic groups also admits a sofic approximation, extending the class of known sofic groups and advancing understanding of their algebraic properties.

Contribution

It provides a construction method for sofic approximations of wreath products, showing that the class of sofic groups is closed under this operation.

Findings

Wreath product of two sofic groups is sofic.

Constructs explicit sofic approximations for wreath products.

Supports the conjecture that all groups are sofic.

Abstract

Given sofic approximations for countable, discrete groups $G,H$, we construct a sofic approximation for their wreath product $G\wr H$.