Abstract.
We give an example of an infinite simple Frobenius group
G without involutions, with a trivial kernel and a nilpotent
complement. Nevertheless, this group is not $\omega $- stable (not
even superstable), this is the "only" property missing in order to
be a counterexample to the Cherlin-Zil'ber Conjecture which says
that simple $\omega $- stable groups are algebraic groups.
Palabras claves. Frobenius groups, group of finite Morley rank, pseudo-bad group, HNN-extension.
