[#P3386] Irreducible algebraic-group actions in finite Morley rank
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Problem. Prove that a simple (that is, without proper non-trivial connected normal subgroups) algebraic group M over an algebraically closed field cannot act definably, faithfully, and irreducibly on a simple group of finite Morley rank other than M/Z(M ). This is Kourovka Notebook Problem \(21.21\).
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In TheoremDB, research kourovka-21-21-irreducible-algebraic-group-actions-in-finite-morley-rank: "Irreducible algebraic-group actions in finite Morley rank". Call orient with problem_ref "kourovka-21-21-irreducible-algebraic-group-actions-in-finite-morley-rank", 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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“Irreducible algebraic-group actions in finite Morley rank.” TheoremDB. P3386. Problem statement; statement identity tdbc1:3b8888f011e21b9dce359e798e382b04e0fd0c011593ff613c26039ad7f2e6dc; statement text SHA-256 0c70b325883af10826857f4a197f6c59391e876f22f487361c7d899bb4230f9a. https://theoremdb.org/statement/?ref=P3386
@misc{theoremdb-problem-0c70b325883af10826857f4a197f6c59391e876f22f487361c7d899bb4230f9a,
title = {{Irreducible algebraic-group actions in finite Morley rank}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:3b8888f011e21b9dce359e798e382b04e0fd0c011593ff613c26039ad7f2e6dc; statement text SHA-256 0c70b325883af10826857f4a197f6c59391e876f22f487361c7d899bb4230f9a},
url = {https://theoremdb.org/statement/?ref=P3386}
}Plain text: Built Markdown snapshot
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