An introduction to hyperlinear and sofic groups

TL;DR

This paper provides an introductory overview of hyperlinear and sofic groups, discussing their definitions, properties, and significance within set theory and group theory, based on lecture notes from a workshop.

Contribution

It offers an accessible introduction and synthesis of hyperlinear and sofic groups, complementing previous surveys and serving as educational material for researchers and students.

Findings

Summarizes key concepts of hyperlinear and sofic groups.

Highlights their relevance in set theory and group theory.

Provides educational insights through lecture notes.

Abstract

This is an edited write-up of lecture notes of the 7-th Appalachian set theory workshop of the same title led by the first named author at the Cornell University on November 22, 2008. A draft version of the notes was prepared by the second named author. This presentation is largely complementary to the earlier survey by the first-named author (Hyperlinear and sofic groups: a brief guide, Bull. Symb. Logic 14 (2008), pp. 449-480; arXiv:0804.3968v8 [math.GR]).