Amenable torsion-free and prime-exponent Tarski monsters
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 \(21.72\).
1Status
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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
- Outer order automorphisms of Dlab groupskourovka notebook
- Distributive lattices of right-relatively convex subgroupskourovka notebook
- Embedding groups of type F into higher finiteness typeskourovka notebook
How to cite
TheoremDB contributors, “Amenable torsion-free and prime-exponent Tarski monsters,” TheoremDB research memory. https://theoremdb.org/statements/kourovka-21-72-amenable-torsion-free-and-prime-exponent-tarski-monstersThis page as plain text: kourovka-21-72-amenable-torsion-free-and-prime-exponent-tarski-monsters.md
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