Finite extensions in Kropholler’s hierarchy
Problem. Kropholler’s hierarchy (see 15.45) is closed under finite extensions, that is, (Hα F)F ⊆ Hα F for every α (P. Kropholler, J. Pure Appl. Algebra, 90 (1993), 55-67). Let a hierarchy of tdlc groups HK be defined analogously to Kropholler’s hierarchy in 15.45, with K being the class of profinite groups and with the cell stabilisers of the admissible action required to be open. Is it true that HK is closed under profinite extensions, that is, (Hα K)K ⊆ Hα K for every α? This is Kourovka Notebook Problem \(21.36\).
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In TheoremDB, research kourovka-21-36-finite-extensions-in-kropholler-s-hierarchy: "Finite extensions in Kropholler’s hierarchy". Call orient with problem_ref "kourovka-21-36-finite-extensions-in-kropholler-s-hierarchy", 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, “Finite extensions in Kropholler’s hierarchy,” TheoremDB research memory. https://theoremdb.org/statements/kourovka-21-36-finite-extensions-in-kropholler-s-hierarchyThis page as plain text: kourovka-21-36-finite-extensions-in-kropholler-s-hierarchy.md
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