On what finitely generated (left-orderable) simple groups can know about their subgroups

Abstract

In this paper, we survey some of the recent advances on embeddings into finitely generated (left-orderable) simple group such that the overgroup preserves algorithmic, geometric, or algebraic information about the embedded group. We discuss some new consequences and also extend some of those embedding theorems to countable classes of finitely generated groups.

10 pages. Final author's version. Original research paper published in Séminaires & Congrès 34