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A construction of 2-arc-transitive non-solvable covers of complete graphs

Jiyong Chen, Cai Heng Li, Ci Xuan Wu, Yan Zhou Zhu

Abstract

We construct connected $2$-arc-transitive covers of complete graphs with non-abelian characteristically simple transformation groups. This solves the existence problem for non-solvable $2$-arc-transitive covers of complete graphs.

A construction of 2-arc-transitive non-solvable covers of complete graphs

Abstract

We construct connected -arc-transitive covers of complete graphs with non-abelian characteristically simple transformation groups. This solves the existence problem for non-solvable -arc-transitive covers of complete graphs.

Paper Structure

This paper contains 3 sections, 7 theorems, 33 equations.

Table of Contents

  1. Introduction
  2. The construction
  3. For the case n=4

Key Result

Theorem 1.2

Let $\Sigma={\mathrm{K}}_n$ be the complete graph of order $n\geqslant 4$. Then, for any finite non-abelian simple group $T$, there exist connected $(X,2)$-arc-transitive covers of $\Sigma$, where $X=T^d{.}{\mathrm{S}}_n$ for some integer $d$, and $T^d$ is minimal normal in $X$. $\blacktriangleleft$

Theorems & Definitions (13)

  • Theorem 1.2
  • Corollary 1.3
  • Example 2.1
  • Lemma 2.2
  • Lemma 2.4
  • proof
  • Lemma 2.5
  • proof
  • Theorem 3.2
  • Lemma 3.3
  • ...and 3 more