1. Groups of finite Morley rank with a generically sharply multiply transitive action
- Author
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Ayşe Berkman and Alexandre V. Borovik
- Subjects
Algebra and Number Theory ,Group (mathematics) ,010102 general mathematics ,Structure (category theory) ,Morley rank ,01 natural sciences ,Action (physics) ,Combinatorics ,20F11, 03C60 ,Dimension (vector space) ,0103 physical sciences ,010307 mathematical physics ,0101 mathematics ,Algebraically closed field ,Abelian group ,Mathematics - Group Theory ,Mathematics ,Vector space - 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 $\operatorname{GL}_n(F)$ 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, Comment: in its final form
- Published
- 2018