[#P3456] Amenable torsion-free and prime-exponent Tarski monsters
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Problem. We say that a group is a Tarski monster if it is finitely generated, not cyclic, and all of its proper non-trivial subgroups are isomorphic to each other. a) Do there exist amenable torsion-free Tarski monsters? b) Do there exist amenable Tarski monsters of prime exponent? This is Kourovka Notebook Problem \(21.72\).
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In TheoremDB, research kourovka-21-72-amenable-torsion-free-and-prime-exponent-tarski-monsters: "Amenable torsion-free and prime-exponent Tarski monsters". Call orient with problem_ref "kourovka-21-72-amenable-torsion-free-and-prime-exponent-tarski-monsters", 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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“Amenable torsion-free and prime-exponent Tarski monsters.” TheoremDB. P3456. Problem statement; statement identity tdbc1:b14119c1470490eacc9973284d246807036b1baf3c701e2420ad1111a400ed13; statement text SHA-256 b42441e26c37377095fe3a6b9de5fdc3a600e6829b9c435b345ab2d446d5b397. https://theoremdb.org/statement/?ref=P3456
@misc{theoremdb-problem-b42441e26c37377095fe3a6b9de5fdc3a600e6829b9c435b345ab2d446d5b397,
title = {{Amenable torsion-free and prime-exponent Tarski monsters}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:b14119c1470490eacc9973284d246807036b1baf3c701e2420ad1111a400ed13; statement text SHA-256 b42441e26c37377095fe3a6b9de5fdc3a600e6829b9c435b345ab2d446d5b397},
url = {https://theoremdb.org/statement/?ref=P3456}
}Plain text: Built Markdown snapshot
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