## Noether’s problem and normalization.(English)Zbl 1055.12501

The author provides a very well-written survey of the current status of the work on Noether’s problem. Let $$k$$ be a field, $$k(x_1,\cdots,x_n)$$ the rational function field in $$n$$ variables, and $$G$$ a finite group acting as automorphisms of $$k(x_1,\cdots,x_n)$$ and permuting the variables, then the question studied is whether the fixed field of the automorphisms is also a rational function field in $$n$$ variables. She nicely presents the work of several researchers, a. o. Noether, Saltman, Swan, Lenstra, Colliot-Thélène, Sansuc, up to the present state. A large bibliography of 85 items is added.

### MSC:

 12F10 Separable extensions, Galois theory 12F20 Transcendental field extensions 01A60 History of mathematics in the 20th century