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\begin{center}{\Huge Model Theory of Algebraic Groups}\end{center}
\begin{center}{\Large Piotr Kowalski}\end{center}
\begin{center}{\Large Wroclaw}\end{center}

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\Large


Assume $G$ is a stable group and $H$ is 
its type definable subgroup generated
by (the set of realizations of) a strong 
type $p$ of element of $G$.
L.Newelski described a procedure of finding 
generic types of $H$ as limit
points of some sequences of types related 
to $p$, in at most 2 steps.
E.Hrushovski pointed out an example (of 
infinite Morley rank), showing
that in general 2 steps are necessary.

We conjecture that in case of algebraic 
groups 1 step is enough.
We show that it is enough to check this 
conjecture for algebraic types.
We rephrase its conjecture in terms of 
algebraic geometry and verify it
for many algebraic groups.

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