Block‐transitive automorphism groups of 2‐(v,k,λ) $(v,k,\lambda )$ designs with (r,k)=1 $(r,k)=1$

Abstract

In 1984, Camina and Gagen gave the result that the block-transitive automorphism group G of a 2-v k ( , , 1)design with  k v must be flag-transitive, moreover, G is point-primitive of affine or almost simple type. As a generalization of this result, the purpose of this paper is to study block-transitive automorphism groups of nontrivial 2-v k λ ( , , ) designs with r k ( , ) = 1, where r is the number of blocks incident with a given point. We prove

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