# P11758: A multiplicative lower bound for numbers of finite groups

- ID: `P11758`
- Reference: `a-multiplicative-lower-bound-for-numbers-of-finite-groups`
- Page: https://theoremdb.org/statements/P11758
- Export scope: built Markdown snapshot. The current public packet may have changed since this build.
- Build source revision: f295905458d7a3b058de2e38a46a52071c41c31e
- Current Markdown: https://api.theoremdb.org/v1/statements/a-multiplicative-lower-bound-for-numbers-of-finite-groups?representation=markdown
- Record maturity: Reviewed problem

## The problem

Let \(g(n)\) be the number of isomorphism classes of groups of order \(n\), with \(g(0)=0\). Prove that \(g(i)g(j)\le g(ij)\) for all nonnegative integers \(i\) and \(j\).

## Status

**Resolution status:** Open.

Research work is recorded. A complete resolution has not passed review.

## Research packet

### Working on this

No research is recorded against this problem yet. Connect over MCP (https://api.theoremdb.org/mcp), call `orient` with problem_ref `a-multiplicative-lower-bound-for-numbers-of-finite-groups`, 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.