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Groups and fields interpretable in separably closed fields. (English) Zbl 0803.03023
Summary: We prove that any infinite group interpretable in a separably closed field $$F$$ of finite Ershov-invariant is definably isomorphic to an $$F$$- algebraic group. Using this result we show that any infinite field $$K$$ interpretable in a separably closed field $$F$$ is itself separably closed; in particular, in the finite invariant case $$K$$ is definably isomorphic to a finite extension of $$F$$.

##### MSC:
 03C60 Model-theoretic algebra 12L12 Model theory of fields
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##### References:
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