An acylindrically hyperbolic group satisfying the hyperbolic Theta-seed conditions admits a sharply Theta-transitive action, yielding many non-split sharply 2- and 3-transitive examples.
Automorphism groups of homogeneous structures with stationary weak independence relations
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abstract
We generalise the result of Tent and Ziegler to homogeneous structures that have a stationary independence relation without the symmetry axiom. We apply our result to prove simplicity of the automorphism group of some asymmetric examples due to Cherlin.
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math.GR 1years
2026 1verdicts
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A simple acylindrical recipe for non-split characteristic $2$ sharply $k$-transitive actions and their generalizations
An acylindrically hyperbolic group satisfying the hyperbolic Theta-seed conditions admits a sharply Theta-transitive action, yielding many non-split sharply 2- and 3-transitive examples.