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On the geometry of sharply 2-transitive groups

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arxiv 2002.05187 v1 pith:NL5VXU4M submitted 2020-02-12 math.GR math.LO

Tim Clausen , Katrin Tent This is my paper · ORCID
classification math.GRmath.LO
keywords sharplytransitivegeometryrankgroupgroupsmorleyalgebraically
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abstract

We show that the geometry associated to certain non-split sharply 2-transitive groups does not contain a proper projective plane. For a sharply 2-transitive group of finite Morley rank we improve known rank inequalities for this geometry and conclude that a sharply 2-transitive group of Morley rank 6 must be of the form $K\rtimes K^*$ for some algebraically closed field $K$.

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  1. A simple acylindrical recipe for non-split characteristic $2$ sharply $k$-transitive actions and their generalizations

    math.GR 2026-08 conditional novelty 7.0 of 10

    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.

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