Dense generators with slow growth
A fixed pair generates a dense subgroup of subexponential growth in the infinite iterated natural degree-five alternating wreath product.
Scope
The proof establishes the logarithmic growth limit for one compatible pair in the full inverse limit. It does not establish an additional proposed explicit growth bound.
Formal record
- Lean statement
- Kourovka/Problems/P21_44/Statement.lean
- Lean proof
- Kourovka/Problems/P21_44/Solution.lean
- Endpoint
- Kourovka.P21_44.notebookStatement
- Source commit
- 5a6b2c18e326b7b0281f00b64cade629acbfe1f5
- Verification
- Integrity passed (verification record)
- Statement review
- Independent review
- Novelty
- No earlier complete solution located in a bounded search (report); no priority claim is made
- Human acceptance
- 16 September 2026, human statement verifier (acceptance record)
- Agent version
- Nilradical v0
Strict verification passed on 16 September 2026 for 6 endpoints: fresh compilation, frozen-statement comparison, a three-axiom policy, and checks by both Lean and Nanoda. Independent statement review passed. Final human statement acceptance was recorded on 2026-09-16 for the linked proof snapshot.
All 551 inventory entries matched the published mathematical source snapshot. Each result has a separate frozen specification and strict verification receipt.
Credit
Two-generator construction, proof and formalization by Nilradical v0. Related growth methods are due to Jérémie Brieussel.
- Nilradical v0 — discovery, proof and formalization
- Sean Eberhard — problem proposer
- Jérémie Brieussel — related growth methods
- Konstantin Slutsky and recurrent-sections-lean contributors — adapted formal foundations
Note
Read the mathematical note, an agent-written account of the result and its proof. It is informal and not refereed.
Cite
Nilradical. Nilradical v0: solution and Lean proof of Kourovka Problem 21.44. Repository snapshot 5a6b2c18e326.
@misc{nilradical_v0_kourovka_21_44,
author = {{Nilradical}},
title = {Nilradical v0: solution and Lean proof of Kourovka Problem 21.44},
year = {2026},
howpublished = {Mathematical result with Lean formalization},
url = {https://github.com/alunik/kourovka-lean/blob/5a6b2c18e326b7b0281f00b64cade629acbfe1f5/Kourovka/Problems/P21_44/README.md},
note = {Source commit 5a6b2c18e326b7b0281f00b64cade629acbfe1f5; Nilradical v0}
}