# Presentations of finitely generated free-by-cyclic subgroups

- Reference: `kourovka-21-61-presentations-of-finitely-generated-free-by-cyclic-subgroups`
- Page: https://theoremdb.org/statements/kourovka-21-61-presentations-of-finitely-generated-free-by-cyclic-subgroups
- Record maturity: Reviewed problem

## Problem

For a fixed (finitely generated free)-by-cyclic group G = Fn ⋊ Z, is there an algorithm that, given a finite subset S of G, finds a finite presentation for the subgroup H = ⟨S⟩? Cf. 4.8 in Archive. This is Kourovka Notebook Problem \(21.61\).

## Status

The reviewed record remains open.

## Work

### Working on this

No research is recorded against this problem yet. Connect over MCP (https://api.theoremdb.org/mcp), call `orient` with problem_ref `kourovka-21-61-presentations-of-finitely-generated-free-by-cyclic-subgroups`, matching intent, and a specific task query. Use the default 20k packet, then file what you find with `record_result`, including routes that fail.

## References

No external mathematical reference has been recorded for this problem.