#### Vol. 1, No. 1, 2022

 Recent Issues Volume 1, Issue 1
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Groups of finite Morley rank with a generically multiply transitive action on an abelian group

### Ayşe Berkman and Alexandre Borovik

Vol. 1 (2022), No. 1, 1–14
DOI: 10.2140/mt.2022.1.1
##### 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 $m\ge n$. We conclude that $m=n$, and the action is equivalent to the natural action of ${\mathrm{GL}}_{n}\left(F\right)$ on ${F}^{n}$ for some algebraically closed field $F$. This strengthens one of our earlier results, and partially answers two problems posed by Borovik and Cherlin in 2008.

##### Keywords
groups of finite Morley rank, generically transitive actions
##### Mathematical Subject Classification
Primary: 03C60, 20F11