Doubly transitive lines II: Almost simple symmetries
Combinatorics
2022-12-27 v2 Information Theory
Group Theory
math.IT
Metric Geometry
Representation Theory
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.
Cite
@article{arxiv.1905.06859,
title = {Doubly transitive lines II: Almost simple symmetries},
author = {Joseph W. Iverson and Dustin G. Mixon},
journal= {arXiv preprint arXiv:1905.06859},
year = {2022}
}