Finite Simple Groups in the Primitive Positive Constructability Poset
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866918156790923264 |
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| author | Meyer, Sebastian Starke, Florian |
| author_facet | Meyer, Sebastian Starke, Florian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06487 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite Simple Groups in the Primitive Positive Constructability Poset Meyer, Sebastian Starke, Florian Group Theory Discrete Mathematics Rings and Algebras 20J99, 08A62 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. |
| title | Finite Simple Groups in the Primitive Positive Constructability Poset |
| topic | Group Theory Discrete Mathematics Rings and Algebras 20J99, 08A62 |
| url | https://arxiv.org/abs/2409.06487 |