On the~Fixed Field of a~Generic Automorphism
Matematičeskie trudy, Tome 4 (2001) no. 1, pp. 25-35

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The notion of an almost generic automorphism is introduced and the fixed field is studied of an almost generic automorphism of a stable field. In particular, it is proven that the fixed field of an almost generic automorphism of a separably closed field is regularly closed and its absolute Galois group is isomorphic to $\widehat{\mathbb Z}$.
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K. Zh. Kudaibergenov. On the~Fixed Field of a~Generic Automorphism. Matematičeskie trudy, Tome 4 (2001) no. 1, pp. 25-35. http://geodesic.mathdoc.fr/item/MT_2001_4_1_a2/