The subgroup identification problem for finitely presented groups

TL;DR

This paper introduces the subgroup identification problem for finitely presented groups, demonstrating its unsolvability in general but solvability within certain subclasses, and explores the concepts of strong and weak effective coherence.

Contribution

It defines the subgroup identification problem and shows its unsolvability in general while establishing solvability in finitely presented locally Hopfian groups, advancing understanding of effective coherence.

Findings

Subgroup identification problem is unsolvable for some finitely presented groups.

It is uniformly solvable in finitely presented locally Hopfian groups.

The work differentiates between strong and weak effective coherence.

Abstract

We introduce the subgroup identification problem, and show that there is a finitely presented group G for which it is unsolvable, and that it is uniformly solvable in the class of finitely presented locally Hopfian groups. This is done as an investigation into the difference between strong and weak effective coherence for finitely presented groups.