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

arXiv eprints
 Pub Date:
 February 2020
 arXiv:
 arXiv:2002.05187
 Bibcode:
 2020arXiv200205187C
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Logic;
 20B22;
 03C60