# Large free-abelian duals of subgroups of integer powers

- Reference: `kourovka-21-13-large-free-abelian-duals-of-subgroups-of-integer-powers`
- Page: https://theoremdb.org/statements/kourovka-21-13-large-free-abelian-duals-of-subgroups-of-integer-powers
- Record maturity: Reviewed problem

## Problem

The group \(\mathbb Z^{\omega}\) has a subgroup whose dual is free abelian of rank \(2^{\aleph_0}\). Does it have a subgroup whose dual is free abelian of a strictly larger rank, with \(2^{2^{\aleph_0}}\) the largest possible rank? This is Kourovka Notebook Problem \(21.13\).

## 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-21-13-large-free-abelian-duals-of-subgroups-of-integer-powers`, 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.