  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
