English

Extremely primitive groups and linear spaces

Combinatorics 2022-11-07 v1 Group Theory

Abstract

A finite non-regular primitive permutation group GG is extremely primitive if a point stabiliser acts primitively on each of its nontrivial orbits. Such groups have been studied for almost a century, finding various applications. The classification of extremely primitive groups was recently completed by Burness and Lee, who relied on an earlier classification of soluble extremely primitive groups by Mann, Praeger and Seress. Unfortunately, there is an inaccuracy in the latter classification. We correct this mistake, and also investigate regular linear spaces which admit groups of automorphisms that are extremely primitive on points.

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Cite

@article{arxiv.2211.02198,
  title  = {Extremely primitive groups and linear spaces},
  author = {Melissa Lee and Gabriel Verret},
  journal= {arXiv preprint arXiv:2211.02198},
  year   = {2022}
}

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11 pages