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 linearly ordered homogeneous structures
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abstract
We apply results proved in [Li19] to the linear order expansions of non-trivial free homogeneous structures and the universal n-linear order for $n\geq 2$, and prove the simplicity of their automorphism groups.
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math.GR 1years
2026 1verdicts
CONDITIONAL 1representative citing papers
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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.