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This paper is a contribution to the classification of all pairs , where is a triple system and is a block‐transitive but not flag‐transitive automorphism group of . We prove that if the socle of is a sporadic or alternating group, then one of the following holds: is a and ; is a and ; is a and or ; is a with and .
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Ding et al. (2024) studied this question.
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