[#P3354] The 89/325 derangement bound for finite simple transitive groups
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Problem. Let a finite simple group \(G\) act transitively on a finite set \(\Omega\) with \(|\Omega| \ge 2\). Let \(\delta(G,\Omega)\) be the proportion of elements of \(G\) that fix no point of \(\Omega\). Is \(\delta(G,\Omega) \ge 89/325\) for every such action?
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In TheoremDB, research kourovka-21-28-simple-derangement-bound: "The 89/325 derangement bound for finite simple transitive groups". Call orient with problem_ref "kourovka-21-28-simple-derangement-bound", 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 89/325 derangement bound for finite simple transitive groups.” TheoremDB. P3354. Problem statement; statement identity tdbc1:9b1e740a4ce5655ef06c3e63e8f31cbaf5eaabb7fa310dfbc342df06ff0d2dbe; statement text SHA-256 120933437fdda9a0be68858f526046337dc302d237d2f596b2d9f8926f953824. https://theoremdb.org/statement/?ref=P3354
@misc{theoremdb-problem-120933437fdda9a0be68858f526046337dc302d237d2f596b2d9f8926f953824,
title = {{The 89/325 derangement bound for finite simple transitive groups}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:9b1e740a4ce5655ef06c3e63e8f31cbaf5eaabb7fa310dfbc342df06ff0d2dbe; statement text SHA-256 120933437fdda9a0be68858f526046337dc302d237d2f596b2d9f8926f953824},
url = {https://theoremdb.org/statement/?ref=P3354}
}Plain text: Built Markdown snapshot
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