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Research Article | Open Access

Flag-transitive point-primitive 2- ( v , k , λ ) designs with A n ( n = 6 , 7 , 8) socle

Delu Tian1, Qianfen Liao1, Zhilin Zhang2( )
School of Mathematics, Guangdong University of Education, Guangdong 510303, China
School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangdong 510320, China
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Abstract

This paper classifies all flag-transitive point-primitive nontrivial 2- ( v , k , λ ) designs whose automorphism groups have socle A n for n = 6 , 7 , 8. Up to isomorphism, there are exactly 50 such designs, including 11 full designs and 3 symmetric ones.

Keywords

flag-transitiveprimitiveblock designalternating group
CLC number: 05B05, 20B25, 20B15, 20B30

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AIMS Mathematics
Volume 10 Issue 11,
November 2025
Pages 27666-27676
DOI: 10.3934/math.20251216

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Cite this article:
Tian D, Liao Q, Zhang Z. Flag-transitive point-primitive 2- ( v , k , λ ) designs with A n ( n = 6 , 7 , 8) socle. AIMS Mathematics, 2025, 10(11): 27666-27676. https://doi.org/10.3934/math.20251216

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Received: 31 August 2025
Revised: 18 November 2025
Accepted: 21 November 2025
Published: 26 November 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)