On Flag-Transitive, Point-Quasiprimitive Symmetric 2-( v, k, λ ) Designs with λ Prime

Yongli Zhang, Jiaxin Shen and Zhilin Zhang ()
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Yongli Zhang: School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou 510665, China
Jiaxin Shen: School of Mathematics and Computational Science, Wuyi University, Jiangmen 529020, China
Zhilin Zhang: School of Mathematical Science, South China Normal University, Guangzhou 510640, China

Mathematics, 2023, vol. 11, issue 24, 1-12

Abstract: This paper contributes to the classification of flag-transitive symmetric 2- ( v , k , λ ) designs with λ prime. We investigate the structure of flag-transitive, point-quasiprimitive automorphism groups ( G ) of such 2-designs by applying the classification of quasiprimitive permutation groups. It is shown that the automorphism groups ( G ) have either an abelian socle or a non-abelian simple socle. Moreover, according to the classification of finite simple groups, we demonstrate that point-quasiprimitivity implies point-primitivity of G , except when the socle of G is P S L n ( q ) .

Keywords: 2-design; automorphism group; quasiprimitivity; flag-transitivity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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