Block-transitive automorphism groups of Steiner 3-designs

An automorphism group of a design is called block-transitive if it acts transitively on the blocks. This paper gives a reduction for Steiner 3-designs admitting a block-transitive automorphism group. We prove that a block-transitive point-primitive automorphism group of a nontrivial Steiner 3-design...

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Bibliographic Details
Published in:Discrete mathematics 2023-10, Vol.346 (10), p.113534, Article 113534
Main Authors: Gan, Yunsong, Liu, Weijun
Format: Article
Language:English
Subjects:
Automorphism group
Block-transitive
Point-primitive
Steiner 3-design
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Summary:An automorphism group of a design is called block-transitive if it acts transitively on the blocks. This paper gives a reduction for Steiner 3-designs admitting a block-transitive automorphism group. We prove that a block-transitive point-primitive automorphism group of a nontrivial Steiner 3-design is either affine or almost simple.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2023.113534