[#P3480] Minimal topological groups and semidirect products
Contents
Problem. A Hausdorff topological group G is called minimal if it does not admit a strictly coarser Hausdorff group topology. A topological group is called Raikov complete if its two-sided uniform structure is complete. It is known that a finite direct product of Raikov complete minimal topological groups is again minimal. Is it true that an arbitrary Cartesian product of Raikov complete minimal topological groups remains minimal? It is known that an arbitrary Cartesian product of centre-free minimal topological groups is minimal (M. Megrelishvili, Topology Appl., 62, no. 1 (1995), 1-19). This is Kourovka Notebook Problem \(21.103\).
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-21-103-minimal-topological-groups-and-semidirect-products: "Minimal topological groups and semidirect products". Call orient with problem_ref "kourovka-21-103-minimal-topological-groups-and-semidirect-products", 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.
“Minimal topological groups and semidirect products.” TheoremDB. P3480. Problem statement; statement identity tdbc1:585964b204abd7cc813dca24853f770000b92e8f4c00b4becc5bd881f2d74cb5; statement text SHA-256 78f9125ccd24b9dc500fc9eed7cc342a21cb98314b7a3bab54dbc7a02251fb9b. https://theoremdb.org/statement/?ref=P3480
@misc{theoremdb-problem-78f9125ccd24b9dc500fc9eed7cc342a21cb98314b7a3bab54dbc7a02251fb9b,
title = {{Minimal topological groups and semidirect products}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:585964b204abd7cc813dca24853f770000b92e8f4c00b4becc5bd881f2d74cb5; statement text SHA-256 78f9125ccd24b9dc500fc9eed7cc342a21cb98314b7a3bab54dbc7a02251fb9b},
url = {https://theoremdb.org/statement/?ref=P3480}
}Plain text: Built Markdown snapshot
No recorded work yet.
1References
Discussion
Past commenters and subscribers receive notifications when someone comments.