A reduction for block-transitive triple systems

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)=A5×A5 and T is the unique TS(25,12).