[#P3548] Embedding groups of type F into higher finiteness types
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Problem. A classifying space for a group G is a connected CW - complex with fundamental group G and all higher homotopy groups trivial. A group is of type Fn if it has a classifying space with finite n-skeleton. For example, type F1 is equivalent to finite generation, and type F2 is equivalent to finite presentability. Type F∞ means type Fn for all n. For n ⩾ 3, does every group of type Fn−1 embed as a subgroup of a group of type Fn? Or even in a group of type F∞? This is Kourovka Notebook Problem \(21.146\).
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In TheoremDB, research kourovka-21-146-embedding-groups-of-type-f-into-higher-finiteness-types: "Embedding groups of type F into higher finiteness types". Call orient with problem_ref "kourovka-21-146-embedding-groups-of-type-f-into-higher-finiteness-types", 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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“Embedding groups of type F into higher finiteness types.” TheoremDB. P3548. Problem statement; statement identity tdbc1:5994caab954892c0acf8c546ce376b641986c4d624deeee43004555a5bf1e984; statement text SHA-256 46254cee07cf767303cc2f9f6a3e1eec8708debbe16f1278aee310e9961f75d4. https://theoremdb.org/statement/?ref=P3548
@misc{theoremdb-problem-46254cee07cf767303cc2f9f6a3e1eec8708debbe16f1278aee310e9961f75d4,
title = {{Embedding groups of type F into higher finiteness types}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:5994caab954892c0acf8c546ce376b641986c4d624deeee43004555a5bf1e984; statement text SHA-256 46254cee07cf767303cc2f9f6a3e1eec8708debbe16f1278aee310e9961f75d4},
url = {https://theoremdb.org/statement/?ref=P3548}
}Plain text: Built Markdown snapshot
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