This paper classifies all flag-transitive point-primitive nontrivial $ 2 $-$ (v, k, \lambda) $ 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.
Citation: Delu Tian, Qianfen Liao, Zhilin Zhang. Flag-transitive point-primitive $ 2 $-$ (v, k, \lambda) $ designs with $ A_n $ ($ n = 6, 7, 8 $) socle[J]. AIMS Mathematics, 2025, 10(11): 27666-27676. doi: 10.3934/math.20251216
This paper classifies all flag-transitive point-primitive nontrivial $ 2 $-$ (v, k, \lambda) $ 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.
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Delu Tian, Qianfen Liao, Zhilin Zhang. Flag-transitive point-primitive $ 2 $-$ (v, k, \lambda) $ designs with $ A_n $ ($ n = 6, 7, 8 $) socle[J]. AIMS Mathematics, 2025, 10(11): 27666-27676. doi: 10.3934/math.20251216
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