[#P3520] Factorizations of odd-order abelian groups
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Problem. Conjecture: Let G be a finite additive abelian group with |G| odd. Then any subset A of G with |A| = n > 2 can be written as {a1,..., an } in such a way that all the sums a1 + a2, a2 + a3,..., an−1 + an, an + a1 are distinct. This is Kourovka Notebook Problem \(21.130\).
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In TheoremDB, research kourovka-21-130-factorizations-of-odd-order-abelian-groups: "Factorizations of odd-order abelian groups". Call orient with problem_ref "kourovka-21-130-factorizations-of-odd-order-abelian-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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“Factorizations of odd-order abelian groups.” TheoremDB. P3520. Problem statement; statement identity tdbc1:28939f403cb3748da862ca25191ad91c22478bb57ffb159c34dbde47d49f2af0; statement text SHA-256 303e2248ac7f3102c4b912dbbbd67bc3e1c12a4091541404dabce82f821952c3. https://theoremdb.org/statement/?ref=P3520
@misc{theoremdb-problem-303e2248ac7f3102c4b912dbbbd67bc3e1c12a4091541404dabce82f821952c3,
title = {{Factorizations of odd-order abelian groups}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:28939f403cb3748da862ca25191ad91c22478bb57ffb159c34dbde47d49f2af0; statement text SHA-256 303e2248ac7f3102c4b912dbbbd67bc3e1c12a4091541404dabce82f821952c3},
url = {https://theoremdb.org/statement/?ref=P3520}
}Plain text: Built Markdown snapshot
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