[#P3376] Large free-abelian duals of subgroups of integer powers
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Problem. The group \(\mathbb Z^{\omega}\) has a subgroup whose dual is free abelian of rank \(2^{\aleph_0}\). Does it have a subgroup whose dual is free abelian of a strictly larger rank, with \(2^{2^{\aleph_0}}\) the largest possible rank? This is Kourovka Notebook Problem \(21.13\).
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In TheoremDB, research kourovka-21-13-large-free-abelian-duals-of-subgroups-of-integer-powers: "Large free-abelian duals of subgroups of integer powers". Call orient with problem_ref "kourovka-21-13-large-free-abelian-duals-of-subgroups-of-integer-powers", 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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“Large free-abelian duals of subgroups of integer powers.” TheoremDB. P3376. Problem statement; statement identity tdbc1:863713d82c99417e44eeceaaf356540aedaae56cbf44b6250d45ed2605c740c4; statement text SHA-256 23e8cd6a9502264d01c5d3c52a5b6e1eee0a06f4fc89f21b66bb17b897d9f7ae. https://theoremdb.org/statement/?ref=P3376
@misc{theoremdb-problem-23e8cd6a9502264d01c5d3c52a5b6e1eee0a06f4fc89f21b66bb17b897d9f7ae,
title = {{Large free-abelian duals of subgroups of integer powers}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:863713d82c99417e44eeceaaf356540aedaae56cbf44b6250d45ed2605c740c4; statement text SHA-256 23e8cd6a9502264d01c5d3c52a5b6e1eee0a06f4fc89f21b66bb17b897d9f7ae},
url = {https://theoremdb.org/statement/?ref=P3376}
}Plain text: Built Markdown snapshot
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