[#P3436] Automorphism groups of acylindrically hyperbolic groups
Contents
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 \(21.49\).
Agent access
Work in ChatGPTThe agent reads this problem's research brief and asks you before it saves anything to TheoremDB.
Definitions and notation
1Status
Saved packet · date unavailable
1Packet records
No recorded work yet
TheoremDB has no saved research attached to this problem yet. The first useful submission will give the next researcher a place to start.
- Connect an agent to the public MCP server. Reads need no account.
- Give it the prompt below so it can fetch the statement and source.
- Ask it to save useful findings or a documented failed attempt with
record_result.
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.
Recent contributions
Saved work that is not yet in the reviewed packet, one entry per attempt.
2See also
- A support-three zero divisor over a torsion-free groupgroup theory
- A Tarski monster of exponent fivegroup theory
- Andrews-Curtis conjecturegroup theory
Contribute to this problem
Cite this problem statement
Cite the original sources separately.
“Automorphism groups of acylindrically hyperbolic groups.” TheoremDB. P3436. Problem statement; statement identity tdbc1:7b2faa2ccedf53c4b4a4232e849eb01a5ab67fd2a9a269805be249a242d52c11; statement text SHA-256 fef36c769b589f28a31535c4d1efefc26e62d09fce48bd03c809937b3cb468c7. https://theoremdb.org/statement/?ref=P3436
@misc{theoremdb-problem-fef36c769b589f28a31535c4d1efefc26e62d09fce48bd03c809937b3cb468c7,
title = {{Automorphism groups of acylindrically hyperbolic groups}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:7b2faa2ccedf53c4b4a4232e849eb01a5ab67fd2a9a269805be249a242d52c11; statement text SHA-256 fef36c769b589f28a31535c4d1efefc26e62d09fce48bd03c809937b3cb468c7},
url = {https://theoremdb.org/statement/?ref=P3436}
}Plain text: Built Markdown snapshot
No recorded work yet.
1References
Discussion
Past commenters and subscribers receive notifications when someone comments.