Flag-transitive 2-(v, k, λ) symmetric designs with (k, λ) = 1 and alternating socle

doi:10.1007/s11464-015-0480-0

Front. Math. China

2015, Vol. 10

Issue (5) : 1483-1496 https://doi.org/10.1007/s11464-015-0480-0

RESEARCH ARTICLE

Flag-transitive 2-(v, k, λ) symmetric designs with (k, λ) = 1 and alternating socle

Yan ZHU¹, Haiyan GUAN², Shenglin ZHOU¹(

)

¹. School of Mathematics, South China University of Technology, Guangzhou 510640, China
². Department of Mathematics, China Three Gorges University, Yichang 443002, China

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Abstract

Consider the flag-transitive 2-(v, k, λ) symmetric designs with (k, λ) = 1. We prove that if $D$ is a nontrivial 2-(v, k, λ) symmetric design with (k, λ) = 1 and G≤Aut( $D$ ) is flag-transitive with Soc(G) = A_n for n≥5, then $D$ is the projective space PG₂(3,2) and G = A₇.

Keywords Symmetric design automorphism group alternating group flagtransitive

Corresponding Author(s): Shenglin ZHOU

Issue Date: 12 October 2015

Cite this article:

Yan ZHU,Haiyan GUAN,Shenglin ZHOU. Flag-transitive 2-(v, k, λ) symmetric designs with (k, λ) = 1 and alternating socle[J]. Front. Math. China, 2015, 10(5): 1483-1496.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-015-0480-0
https://academic.hep.com.cn/fmc/EN/Y2015/V10/I5/1483

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