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Block-transitive, point-primitive Steiner 3-designs

Combinatorics 2024-08-28 v3 Group Theory
Authors: Yunsong Gan , Weijun Liu
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Abstract

This paper studies the long-standing open problem of the reduction of Steiner 3-designs admitting a block-transitive automorphism group. We prove that if G acts as a point-primitive, block-transitive automorphism group of a nontrivial Steiner 3-design, then G is of affine or almost simple type.

Keywords

flag-transitive designs permutation groups automorphism groups

Cite

@article{arxiv.2112.00466,
  title  = {Block-transitive, point-primitive Steiner 3-designs},
  author = {Yunsong Gan and Weijun Liu},
  journal= {arXiv preprint arXiv:2112.00466},
  year   = {2024}
}

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