Complete Classification of Flag-Transitive Point-Primitive $2$-Designs with Socle $M_{11}$
Received:October 14, 2019  Revised:April 23, 2020
Key Word: 2-design   flag-transitive   point-primitive   Mathieu group  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11801092), the Characteristic Innovation Project (Natural Science) of Guangdong Province (Grant No.2018KTSCX160) and the Fund of Guangzhou Science and Technology (Grant No.201804010088).
Author NameAffiliation
Delu TIAN Department of Mathematics, Guangdong University of Education, Guangdong 510303, P. R. China 
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      In recent years several authors have determined some 2-designs with flag-transitive point-primitive automorphism group $G$ of almost simple type with sporadic socle. Here we obtain the complete classification of flag-transitive point-primitive non-trivial $2$-designs with socle $M_{11}$, and find that there are precisely 14 such nonisomorphic 2-designs.
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