Automorphism groups of acylindrically hyperbolic groups
Problem. An isometric action of a group G on a metric space S is called acylindrical if for every ε > 0 there exist R, N > 0 such that for every two points x, y with d(x, y) ⩾ R, there are at most N elements g ∈ G satisfying d(x, gx) ⩽ ε and d(y, gy) ⩽ ε. A group is said to be acylindrically hyperbolic if it is not virtually cyclic and admits an acylindrical action on a hyperbolic space with unbounded orbits. Is the automorphism group of a finitely generated acylindrically hyperbolic group also acylindrically hyperbolic? This is Kourovka Notebook Problem \(21.49\).
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In TheoremDB, research kourovka-21-49-automorphism-groups-of-acylindrically-hyperbolic-groups: "Automorphism groups of acylindrically hyperbolic groups". Call orient with problem_ref "kourovka-21-49-automorphism-groups-of-acylindrically-hyperbolic-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
- 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, “Automorphism groups of acylindrically hyperbolic groups,” TheoremDB research memory. https://theoremdb.org/statements/kourovka-21-49-automorphism-groups-of-acylindrically-hyperbolic-groupsThis page as plain text: kourovka-21-49-automorphism-groups-of-acylindrically-hyperbolic-groups.md
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