[#P3400] The Haagerup property for one-relator groups
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Problem. A discrete group G is said to have the Haagerup property (also known as Gromov’s a-T-menability property) if there exists a metrically proper isometric action of G on a (possibly infinite-dimensional) Hilbert space. Are all 1-relator groups Haagerup groups? This is Kourovka Notebook Problem \(21.30\).
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In TheoremDB, research kourovka-21-30-the-haagerup-property-for-one-relator-groups: "The Haagerup property for one-relator groups". Call orient with problem_ref "kourovka-21-30-the-haagerup-property-for-one-relator-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.
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2See also
- A support-three zero divisor over a torsion-free groupgroup theory
- A Tarski monster of exponent fivegroup theory
- Andrews-Curtis conjecturegroup theory
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“The Haagerup property for one-relator groups.” TheoremDB. P3400. Problem statement; statement identity tdbc1:988b0f6e320816952d232c5fff9ccf935299a5fac91c07296be992a78324bdb4; statement text SHA-256 23b86fa695e841b5986382eb70f0a58b71d0105dca11c1b97ce9dcab6605c831. https://theoremdb.org/statement/?ref=P3400
@misc{theoremdb-problem-23b86fa695e841b5986382eb70f0a58b71d0105dca11c1b97ce9dcab6605c831,
title = {{The Haagerup property for one-relator groups}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:988b0f6e320816952d232c5fff9ccf935299a5fac91c07296be992a78324bdb4; statement text SHA-256 23b86fa695e841b5986382eb70f0a58b71d0105dca11c1b97ce9dcab6605c831},
url = {https://theoremdb.org/statement/?ref=P3400}
}Plain text: Built Markdown snapshot
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