Primitive permutation groups of finite Morley rank and affine type
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916510442717184 |
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| author | Berkman, Ayşe Borovik, Alexandre |
| author_facet | Berkman, Ayşe Borovik, Alexandre |
| contents | We give a review of one of the lines in development of the theory of groups of finite Morley rank. These groups naturally appear in model theory as model-theoretic analogues of Galois groups, therefore their actions and their role as permutation groups is of primary interest. We restrict our story to the study of connected groups of finite Morley rank $G$ acting in a definably primitive way on a set $X$ and containing a definable abelian normal subgroup $V$ which acts on $X$ regularly -- the so-called \emph{primitive groups of affine type}. For reasons explained in the paper, this case plays a central role in the theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07307 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Primitive permutation groups of finite Morley rank and affine type Berkman, Ayşe Borovik, Alexandre Group Theory Logic 20F11, 03C60 We give a review of one of the lines in development of the theory of groups of finite Morley rank. These groups naturally appear in model theory as model-theoretic analogues of Galois groups, therefore their actions and their role as permutation groups is of primary interest. We restrict our story to the study of connected groups of finite Morley rank $G$ acting in a definably primitive way on a set $X$ and containing a definable abelian normal subgroup $V$ which acts on $X$ regularly -- the so-called \emph{primitive groups of affine type}. For reasons explained in the paper, this case plays a central role in the theory. |
| title | Primitive permutation groups of finite Morley rank and affine type |
| topic | Group Theory Logic 20F11, 03C60 |
| url | https://arxiv.org/abs/2405.07307 |