In this paper, we study block-transitive automorphism groups of t-\((k^2,k,\lambda )\) designs. We prove that a block-transitive automorphism group G of a t-\((k^2,k,\lambda )\) design must be point-primitive, and G is either an affine group or an almost simple group. Moreover, the nontrivial t-\((k^2,k,\lambda )\) designs admitting block-transitive automorphism groups of almost simple type with sporadic socle and alternating socle are classified.

中文翻译：

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块传递 t- $$(k^2,k,\lambda )$$ 设计的简化

在本文中，我们研究t - \((k^2,k,\lambda )\)设计的块传递自同构群。我们证明t - \((k^2,k,\lambda )\)设计的块传递自同构群G必须是点原语，并且G要么是仿射群，要么是近单群。此外，对承认具有零星底和交替底的几乎简单类型的块传递自同构群的非平凡t - \((k^2,k,\lambda )\)设计进行了分类。