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September 24, 2025Open Access

Classification of flag-transitive 2- (v, k, λ) designs with alternating group Aₙ (n 10) as socle

Key Points

Eighty-seven different flag-transitive designs are identified, improving the classification theory of 2-designs with alternating group action.
The study focuses on point-primitive non-trivial 2-designs, revealing significant insights into their automorphism groups.
These findings provide a reference for future research on designs influenced by almost simple groups.
The results enrich existing knowledge about the structure and classification of 2-designs in combinatorial design theory.

Abstract

This paper is devoted to the classification of all flag-transitive point-primitive non-trivial 2- (v, k, λ) designs with the alternating group Aₙ (n 10) as the socle of their automorphism groups, and 87 different designs are obtained up to isomorphism. The results of this study further improve the classification theory of designs under the action of almost simple groups, and provide reference for the follow-up study of similar problems.

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