Flag-transitive non-symmetric 2-designs with $ \lambda $ prime and exceptional groups of Lie type

Yongli Zhang; Jiaxin Shen; Yongli Zhang; Jiaxin Shen

doi:10.3934/math.20241252

AIMS Mathematics

2024, Volume 9, Issue 9: 25636-25645. doi: 10.3934/math.20241252

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Research article

Flag-transitive non-symmetric 2-designs with $ \lambda $ prime and exceptional groups of Lie type

Yongli Zhang ¹,
Jiaxin Shen ^{2
,
,}

1.
School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou 510665, China
2.
School of Mathematics and Computational Science, Wuyi University, Jiangmen 529020, China

Received: 11 July 2024 Revised: 23 August 2024 Accepted: 26 August 2024 Published: 04 September 2024
MSC : 05B05, 05B25, 20B25

This paper contributes to the classification of flag-transitive 2-$ (v, k, \lambda) $ designs. Let $ \mathcal{D} $ be a non-trivial and non-symmetric $ 2 $-$ (v, k, \lambda) $ design with $ \lambda $ prime and $ G $ be a flag-transitive point-primitive automorphism group of $ \mathcal{D} $. A recent work by the first author and Chen has proven that the socle of $G$ is either a nonabelian simple group or an elementary abelian $ p $-group for some prime $ p $. In this paper, we focus on the case where the socle of $G$ is an exceptional group of Lie type and give all possible parameters of such 2-designs.
- 2-design,
- flag-transitive,
- exceptional group of Lie type,
- primitive group
Citation: Yongli Zhang, Jiaxin Shen. Flag-transitive non-symmetric 2-designs with $ \lambda $ prime and exceptional groups of Lie type[J]. AIMS Mathematics, 2024, 9(9): 25636-25645. doi: 10.3934/math.20241252

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Abstract

This paper contributes to the classification of flag-transitive 2-$ (v, k, \lambda) $ designs. Let $ \mathcal{D} $ be a non-trivial and non-symmetric $ 2 $-$ (v, k, \lambda) $ design with $ \lambda $ prime and $ G $ be a flag-transitive point-primitive automorphism group of $ \mathcal{D} $. A recent work by the first author and Chen has proven that the socle of $G$ is either a nonabelian simple group or an elementary abelian $ p $-group for some prime $ p $. In this paper, we focus on the case where the socle of $G$ is an exceptional group of Lie type and give all possible parameters of such 2-designs.

References

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