Groups of finite Morley rank with a generically multiply transitive action on an abelian group

Ayşe Berkman; Alexandre Borovik

doi:10.2140/mt.2022.1.1

Groups of finite Morley rank with a generically multiply transitive action on an abelian group

Group Theory 2022-07-20 v2 Logic

Authors: Ayşe Berkman , Alexandre Borovik

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Abstract

We investigate the configuration where a group of finite Morley rank acts definably and generically $m$ -transitively on an elementary abelian $p$ -group of Morley rank $n$ , where $p$ is an odd prime, and $m\geqslant n$ . We conclude that $m=n$ , and the action is equivalent to the natural action of $\operatorname{GL}_n(F)$ on $F^n$ for some algebraically closed field $F$ . This strengthens our earlier result in arXiv:1802.05222, and partially answers two problems posed in [9].

Keywords

groups of finite morley rank generic m-transitivity elementary abelian p-group algebraically closed field gl_n natural action

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@article{arxiv.2107.09997,
  title  = {Groups of finite Morley rank with a generically multiply transitive action on an abelian group},
  author = {Ayşe Berkman and Alexandre Borovik},
  journal= {arXiv preprint arXiv:2107.09997},
  year   = {2022}
}

Comments

To appear in \textit{Model Theory}. The manuscript will undergo copy editing, typesetting, and review of the resulting proof before it is published

Groups of finite Morley rank with a generically multiply transitive action on an abelian group

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