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Some remarks on sharply 2-transitive groups and near-domains

Frank Wagner

Abstract

A sharply 2-transitive permutation group of characteristic 0 whose point stabiliser has an abelian subgroup of finite index splits. More generally, a near-domain of characteristic 0 with a multiplicative subgroup of finite index avoiding all multipliers $d_{a,b}$ must be a near-field. In particular this answers question 12.48 b) of the Kourovka Notebook in characteristic 0.

Some remarks on sharply 2-transitive groups and near-domains

Abstract

A sharply 2-transitive permutation group of characteristic 0 whose point stabiliser has an abelian subgroup of finite index splits. More generally, a near-domain of characteristic 0 with a multiplicative subgroup of finite index avoiding all multipliers must be a near-field. In particular this answers question 12.48 b) of the Kourovka Notebook in characteristic 0.
Paper Structure (2 sections, 3 theorems, 3 equations)

This paper contains 2 sections, 3 theorems, 3 equations.

Table of Contents

  1. Introduction
  2. Near-domains and near-fields.

Key Result

Lemma 4

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

Theorems & Definitions (7)

  • Definition 1
  • Lemma 4
  • proof
  • Proposition 5
  • proof
  • Corollary 6
  • proof