The paper reports on an investigation of structure of block-transitive automorphism groups of a triple system. We prove that if G is a block-transitive automorphism group of a triple system T , then G cannot be of simple diagonal or twisted wreath product type. Furthermore, if G is of product type, then Soc ( G ) = A 5 × A 5 and T is the unique T S ( 25 , 12 ) .
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