Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Sharply 2-transitive groups of finite Morley rank

Tuna Altinel, Ayse Berkman, Frank Olaf Wagner

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 0 splits if its point stabilizers are virtually abelian.

Sharply 2-transitive groups of finite Morley rank

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 0 splits if its point stabilizers are virtually abelian.

Paper Structure

This paper contains 5 sections, 9 theorems, 7 equations.

Table of Contents

  1. Introduction
  2. Near-domains and near-fields.
  3. Characteristic $2$
  4. Centrality of the Sylow $2$-Subgroup
  5. Characteristic $\not=2$

Key Result

Lemma 2.4

Suppose $d_{a,1/k}=1$. Then $d_{a,n/k}=1$ for all $n\in\mathbb N$.

Theorems & Definitions (24)

  • Conjecture 1.1
  • Definition 2.1
  • Lemma 2.4
  • proof
  • Proposition 2.5
  • proof
  • Corollary 2.6
  • proof
  • Theorem 3.1
  • proof
  • ...and 14 more