On the geometry of sharply 2-transitive groups
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 $K$.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2020
- DOI:
- 10.48550/arXiv.2002.05187
- arXiv:
- arXiv:2002.05187
- Bibcode:
- 2020arXiv200205187C
- Keywords:
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- Mathematics - Group Theory;
- Mathematics - Logic;
- 20B22;
- 03C60