August 11, 2025Open Access

Flag-Transitive Point-Primitive Quasi-Symmetric 2-Designs and Exceptional Groups of Lie Type

Key Points

The study concludes that socles of automorphism groups cannot be finite simple exceptional groups of Lie type, ensuring structural integrity.
Key evidence shows that the conditions for automorphism groups of quasi-symmetric 2-designs are not met by exceptional types.
Analysis focuses on flag-transitive and point-primitive groups, determining constraints in the context of group theory.
These findings support broader implications in classification of automorphism groups and their symmetry structures.

Abstract

Let D be a non-trivial quasi-symmetric 2-design with two block intersection numbers x=0 and 2 y10, and suppose that G is an automorphism group of D. If G is flag-transitive and point-primitive, then it is known that G is either of affine type or almost simple type. In this paper, we show that the socle of G cannot be a finite simple exceptional group of Lie type.

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Cite This Study

Jianbing Lu (Thu,) studied this question.

synapsesocial.com/papers/68a35ee30a429f7973327be7 https://doi.org/https://doi.org/10.37236/13529

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