# Coherence of free pro-p products with amalgamation

- Reference: `kourovka-21-141-coherence-of-free-pro-p-products-with-amalgamation`
- Page: https://theoremdb.org/statements/kourovka-21-141-coherence-of-free-pro-p-products-with-amalgamation
- Record maturity: Reviewed problem

## Problem

Let G = G1 ⨿H G2 be a free pro-p product of coherent pro-p groups with polycyclic amalgamation. Is G coherent? For abstract groups this is known to be true. A group is said to be coherent if each of its finitely generated subgroups is finitely presented, and in the question the coherency is used in the pro-p sense. This is Kourovka Notebook Problem \(21.141\).

## 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-21-141-coherence-of-free-pro-p-products-with-amalgamation`, 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.