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Locally 2-homogeneous block designs

Jianfu Chen, Peice Hua, Cai Heng Li, Yanni Wu

Abstract

We extend Kantor's classification of 2-transitive symmetric designs (1985) to a classification of locally 2-homogeneous designs.

Locally 2-homogeneous block designs

Abstract

We extend Kantor's classification of 2-transitive symmetric designs (1985) to a classification of locally 2-homogeneous designs.
Paper Structure (8 sections, 19 theorems, 71 equations, 3 tables)

This paper contains 8 sections, 19 theorems, 71 equations, 3 tables.

Table of Contents

  1. Introduction
  2. Locally 2-homogeneous designs
  3. Infinite families
  4. The symmetric case
  5. The affine case
  6. $G \leqslant {\rm A\Gamma L}_1(p^f)$
  7. $G \not\leqslant {\rm A\Gamma L}_1(p^f)$
  8. The almost simple case

Key Result

Theorem 1.2

Let ${\mathcal{D}}=({\mathcal{P}},{\mathcal{B}},{\mathcal{I}})$ be a $G$-locally $2$-homogeneous design. Then $G$ is $2$-homogeneous on ${\mathcal{P}}$, and either (1) or (2) occurs. (1)$G$ is locally $2$-transitive on ${\mathcal{D}}$ and $2$-transitive on ${\mathcal{P}}$. One of the following holds (2)$G$ is not locally $2$-transitive on ${\mathcal{D}}$. In this case, ${\mathcal{D}}$ and $(G,G_\

Theorems & Definitions (39)

  • Definition 1.1
  • Theorem 1.2
  • Lemma
  • Lemma 2.1
  • proof
  • Lemma 2.3
  • proof
  • Lemma 2.4
  • proof
  • Lemma 2.5
  • ...and 29 more