Groups of finite Morley rank with a generically sharply multiply transitive action

Abstract

We prove that if $G$ is a group of finite Morley rank which acts definably and generically sharply $n$-transitively on a connected abelian group $V$ of Morley rank $n$ with no involutions, then there is an algebraically closed field $F$ of characteristic $\ne 2$ such that $V$ has a structure of a vector space of dimension $n$ over $F$ and $G$ acts on $V$ as the group ${\mathrm{GL}}_n(F)$ in its natural action on $F^n$. This is the final pre-publication version of the paper: A. Berkman and A. Borovik, Groups of finite Morley rank with a generically sharply multiply transitive action, J. Algebra (2018), https://doi.org/10.1016/j.jalgebra.2018.07.033. Accepted for publication 28 July 2018. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published

arXiv commentin its final form

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• Generically multiple transitive algebraic group actions
• On analogies between algebraic groups and groups of finite Morley rank
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Cited by in corpus (2)

• Finite group actions on abelian groups of finite Morley rank
• Groups of finite Morley rank with a generically multiply transitive action on an abelian group