# Doubly transitive lines II: Almost simple symmetries

## TL;DR

This paper classifies complex lines with doubly transitive automorphism groups exhibiting almost simple symmetries, using Schur covers, and extends the classification to linearly dependent cases in real and complex spaces.

## Contribution

It introduces a novel method involving Schur covers to classify doubly transitive lines with almost simple symmetries and extends existing classifications to dependent lines.

## Key findings

- Classification of doubly transitive lines with almost simple symmetries
- A general recipe using Schur covers for recovering lines from automorphism groups
- Complete classification of linearly dependent doubly transitive lines in real and complex spaces

## Abstract

We study lines through the origin of finite-dimensional complex vector spaces that enjoy a doubly transitive automorphism group. This paper classifies those lines that exhibit almost simple symmetries. We introduce a general recipe involving Schur covers to recover doubly transitive lines from their automorphism group. Combining our results with recent work on the affine case by Dempwolff and Kantor, we deduce a classification of all linearly dependent doubly transitive lines in real or complex space.