[#P3532] Power subgroups in finite p-groups
Contents
Problem. If the p-th powers in a finite p-group form a subgroup, must that subgroup be powerful? That is, for p ̸= 2, if the p-th powers in a p-group of exponent p2 form a subgroup, must that subgroup be abelian? For a 2-group of exponent 8, if the squares form a subgroup, must that subgroup be abelian? This is Kourovka Notebook Problem \(21.137\).
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-21-137-power-subgroups-in-finite-p-groups: "Power subgroups in finite p-groups". Call orient with problem_ref "kourovka-21-137-power-subgroups-in-finite-p-groups", 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.
“Power subgroups in finite p-groups.” TheoremDB. P3532. Problem statement; statement identity tdbc1:1988005bec56b53faa4dbc8e378a15a879653f85f2ca8288efe0859295ec1616; statement text SHA-256 0d5fce3a38c20221e8ff03ed108a79793a7702a87d7ae0db9730aca6754711b9. https://theoremdb.org/statement/?ref=P3532
@misc{theoremdb-problem-0d5fce3a38c20221e8ff03ed108a79793a7702a87d7ae0db9730aca6754711b9,
title = {{Power subgroups in finite p-groups}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:1988005bec56b53faa4dbc8e378a15a879653f85f2ca8288efe0859295ec1616; statement text SHA-256 0d5fce3a38c20221e8ff03ed108a79793a7702a87d7ae0db9730aca6754711b9},
url = {https://theoremdb.org/statement/?ref=P3532}
}Plain text: Built Markdown snapshot
No recorded work yet.
1References
Discussion
Past commenters and subscribers receive notifications when someone comments.