4 problems

Let $(G,V)$ be a faithful module of finite Morley rank, and suppose that $V$ has Morley rank $n$ and $G$ is generically $n$-transitive. Highly generically transitive module conject…

Let $(G,V)$ be a module of finite Morley rank, with $G$ connected and simple modulo its at most finite centre. Suppose that $G$ is transitive on $V\setminus\{0\}$ and generically…

Let $G$ be a connected group of finite Morley rank acting faithfully, definably and transitively on a set $X$ of Morley rank $n$, and suppose the action is generically $(n+2)$-tran…

Let $(G,X)$ be a faithful definable permutation group of finite Morley rank, let $G$ be connected and definably primitive on $X$, and let $b(G)$ denote the minimal cardinality of a…