Sofic groups: graph products and graphs of groups

TL;DR

This paper proves that certain constructions of sofic groups, specifically graph products and graphs of groups with sofic vertex groups and amenable edge groups, preserve the property of being sofic.

Contribution

It establishes that graph products of sofic groups and graphs of groups with specific conditions are also sofic, expanding the class of known sofic groups.

Findings

Graph products of sofic groups are sofic.

Graphs of groups with sofic vertex groups and amenable edge groups are sofic.

The results extend the understanding of how soficity is preserved under group constructions.

Abstract

We prove that graph products of sofic groups are sofic, as are graphs of groups for which vertex groups are sofic and edge groups are amenable.