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.
arXiv preprint arXiv:2509.11958 , year=
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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.