[#P3492] Tau-automorphisms of finite simple groups
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Problem. Let S be a finite simple nonabelian group that is not isomorphic to any group B2 (q). A nonidentity automorphism x of S is called a τ -automorphism if every two conjugates of x in ⟨x, Inn(S)⟩ generate a subgroup of order not divisible by 3. If S admits a τ -automorphism, we call S a τ -group. (a) List all τ -groups up to isomorphism. (b) Do τ -automorphisms of odd order exist? This is Kourovka Notebook Problem \(21.111\).
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In TheoremDB, research kourovka-21-111-tau-automorphisms-of-finite-simple-groups: "Tau-automorphisms of finite simple groups". Call orient with problem_ref "kourovka-21-111-tau-automorphisms-of-finite-simple-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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“Tau-automorphisms of finite simple groups.” TheoremDB. P3492. Problem statement; statement identity tdbc1:1feefca8d4cefada11381fb9447fafcf4d190a5a064250856b7e980dd2315257; statement text SHA-256 1dc656162a899b12f7bf9a60b4df8095bf6fab2a24528f7b0276e2317e1ac004. https://theoremdb.org/statement/?ref=P3492
@misc{theoremdb-problem-1dc656162a899b12f7bf9a60b4df8095bf6fab2a24528f7b0276e2317e1ac004,
title = {{Tau-automorphisms of finite simple groups}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:1feefca8d4cefada11381fb9447fafcf4d190a5a064250856b7e980dd2315257; statement text SHA-256 1dc656162a899b12f7bf9a60b4df8095bf6fab2a24528f7b0276e2317e1ac004},
url = {https://theoremdb.org/statement/?ref=P3492}
}Plain text: Built Markdown snapshot
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