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arXiv · 2409.06487

Finite Simple Groups in the Primitive Positive Constructability Poset

Sebastian Meyer·Florian Starke
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Abstract

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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Sebastian Meyer, Florian Starke. 2024-09-10. Finite Simple Groups in the Primitive Positive Constructability Poset. https://arxiv.org/abs/2409.06487

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