Block‐Transitive and Point‐Primitive 2‐ Designs with Sporadic Socle |
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| Authors: | Xiaohong Zhang Shenglin Zhou |
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| Institution: | 1. School of Mathematics, South China University of Technology, Guangzhou, P.R. China;2. School of Mathematics, South China University of Technology, Guangzhou, P.R. ChinaCorresponding author. This work is supported by the National Natural Science Foundation of China (Grant No.11471123). |
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| Abstract: | The purpose of this paper is to classify all pairs  , where  is a nontrivial 2‐ design, and  acts transitively on the set of blocks of  and primitively on the set of points of  with sporadic socle. We prove that there exists only one such pair  :  is the unique 2‐(176,8,2) design and  , the Higman–Sims simple group. |
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| Keywords: | 2‐design block‐transitive design point‐primitive design socle sporadic simple group |
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, where 
is a nontrivial 2‐
design, and 
acts transitively on the set of blocks of 
and primitively on the set of points of 
with sporadic socle. We prove that there exists only one such pair 
: 
is the unique 2‐(176,8,2) design and 
, the Higman–Sims simple group.