Finite group actions on abelian groups of finite Morley rank
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866916331966693376 |
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| author | Borovik, Alexandre |
| author_facet | Borovik, Alexandre |
| contents | This paper develops some general results about actions of finite groups on (infinite) abelian groups in the finite Morley rank category. They are linked to a range of problems on groups of finite Morley rank discussed in [16]. Crucially, these results are needed for the forthcoming work by Ayşe Berkman and myself [5] where we remove the `sharpness' assumption from [4]. Also, they yield a proof of the long standing conjecture of linearity of irreducible definable actions of simple algebraic groups on elementary abelian $p$-groups of finite Morley rank [16, Conjecture 12]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_00604 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Finite group actions on abelian groups of finite Morley rank Borovik, Alexandre Group Theory 20F11 This paper develops some general results about actions of finite groups on (infinite) abelian groups in the finite Morley rank category. They are linked to a range of problems on groups of finite Morley rank discussed in [16]. Crucially, these results are needed for the forthcoming work by Ayşe Berkman and myself [5] where we remove the `sharpness' assumption from [4]. Also, they yield a proof of the long standing conjecture of linearity of irreducible definable actions of simple algebraic groups on elementary abelian $p$-groups of finite Morley rank [16, Conjecture 12]. |
| title | Finite group actions on abelian groups of finite Morley rank |
| topic | Group Theory 20F11 |
| url | https://arxiv.org/abs/2008.00604 |