BooksmlmCollected Volumepp. 1–12

Sharply 2-transitive groups of finite Morley rank

  • Tuna Altınel

    Université Claude Bernard Lyon 1, CNRS, Villeurbanne, France

  • Ayşe Berkman

    Mimar Sinan Güzel Sanatlar Üniversitesi, Istanbul, Turkey

  • Frank O. Wagner

    Université Claude Bernard Lyon 1, CNRS, Villeurbanne, France
Sharply 2-transitive groups of finite Morley rank cover
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Abstract

A sharply 2-transitive permutation group of finite Morley rank and characteristic 2 splits; a split sharply 2-transitive permutation group of finite Morley rank and characteristic different from 2 is the group of affine transformations of an algebraically closed field. In particular, a sharply 2-transitive permutation group of finite Morley rank of characteristic 3 is the group of affine transformations of an algebraically closed field of characteristic 3. Without any assumption on Morley rank, a sharply 2-transitive permutation group of characteristic splits if its point stabilizers are virtually abelian.