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This article is a contribution to the study of the automorphism groups of  designs. Let be a non-trivial  design where for some positive integer , and  is block-transitive. If the socle of G is isomorphic to the simple groups of lie type, then G is not flag-transitive.

Block-Transitive 4-(<i>v</i>,<i>k</i>,4) Designs and Ree Groups