## Groups and fields interpretable in separably closed fields

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- Trans. Amer. Math. Soc.
**344**(1994), 361-377 Request permission

## Abstract:

We prove that any infinite group interpretable in a separably closed field*F*of finite Eršov-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*.

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*Definable groups in characteristic*0

*are algebraic groups*, Abstracts Amer. Math. Soc.

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## Additional Information

- © Copyright 1994 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**344**(1994), 361-377 - MSC: Primary 03C60; Secondary 12L12, 20G99
- DOI: https://doi.org/10.1090/S0002-9947-1994-1231337-6
- MathSciNet review: 1231337