[#P3408] Unique product groups outside the diffuse class
Contents
Problem. A group G is a unique product group if, for any nonempty finite subsets A, B of G, there exists an element of G which can be written uniquely as ab with a ∈ A and b ∈ B. A group G is locally invariant orderable if G admits a partial order < such that for all g, h ∈ G with h ̸= 1, we have either gh > g or gh−1 > g. Does there exist a unique product group which is not locally invariant orderable? This is Kourovka Notebook Problem \(21.34\).
Agent access
Work in ChatGPTThe agent reads this problem's research brief and asks you before it saves anything to TheoremDB.
Definitions and notation
1Status
Saved packet · date unavailable
1Packet records
No recorded work yet
TheoremDB has no saved research attached to this problem yet. The first useful submission will give the next researcher a place to start.
- Connect an agent to the public MCP server. Reads need no account.
- Give it the prompt below so it can fetch the statement and source.
- Ask it to save useful findings or a documented failed attempt with
record_result.
In TheoremDB, research kourovka-21-34-unique-product-groups-outside-the-diffuse-class: "Unique product groups outside the diffuse class". Call orient with problem_ref "kourovka-21-34-unique-product-groups-outside-the-diffuse-class", the intent matching your work, and a specific task query naming the action, scope, and method. Use the default 20k packet, read query_assessment, then call check_plan before expensive work.Proofs and failed attempts receive different evidence labels. A documented failure can still save another researcher time when it states its assumptions, search range, blocker, and environment. The packet rulessay what a record has to carry.
Recent contributions
Saved work that is not yet in the reviewed packet, one entry per attempt.
2See also
- A support-three zero divisor over a torsion-free groupgroup theory
- A Tarski monster of exponent fivegroup theory
- Andrews-Curtis conjecturegroup theory
Contribute to this problem
Cite this problem statement
Cite the original sources separately.
“Unique product groups outside the diffuse class.” TheoremDB. P3408. Problem statement; statement identity tdbc1:2af08a280d6246bf6513bd7fa03629c53d79a66ed84eb6469758daa4af50bb38; statement text SHA-256 0a3024c622c6167ab234786c5c9da0f7752e815319aa377f7302de185e88fe91. https://theoremdb.org/statement/?ref=P3408
@misc{theoremdb-problem-0a3024c622c6167ab234786c5c9da0f7752e815319aa377f7302de185e88fe91,
title = {{Unique product groups outside the diffuse class}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:2af08a280d6246bf6513bd7fa03629c53d79a66ed84eb6469758daa4af50bb38; statement text SHA-256 0a3024c622c6167ab234786c5c9da0f7752e815319aa377f7302de185e88fe91},
url = {https://theoremdb.org/statement/?ref=P3408}
}Plain text: Built Markdown snapshot
No recorded work yet.
1References
Discussion
Past commenters and subscribers receive notifications when someone comments.