原始正构造性 Poset 中的有限简单群

Sebastian Meyer, Florian Starke
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引用次数: 0

摘要

我们证明,任何在有限域上具有准马尔采夫运算和所有弧度的完全对称运算的克隆体,都有一个从 I(双元素集上所有幂等运算的克隆体)传入的 minionhomomorphism。我们利用这一结果来证明,在pp-可构造性正集中,具有在I下不变的所有关系的结构的下盖是三个顶点上的传递锦标赛,以及与所有有限单纯群一一对应的结构。
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Finite Simple Groups in the Primitive Positive Constructability Poset
We show that any clone over a finite domain that has a quasi Maltsev operation and fully symmetric operations of all arities has an incoming minion homomorphism from I, the clone of all idempotent operations on a two element set. We use this result to show that in the pp-constructability poset the lower covers of the structure with all relations that are invariant under I are the transitive tournament on three vertices and structures in one-to-one correspondence with all finite simple groups.
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