Mathematical Notes

, Volume 86, Issue 5–6, pp 625–628 | Cite as

On the saturation of subfields of invariants of finite groups

  • I. V. Arzhantsev
  • A. P. Petravchuk


Every subfield \( \mathbb{K} \)(φ) of the field of rational fractions \( \mathbb{K} \)(x 1,..., x n ) is contained in a unique maximal subfield of the form \( \mathbb{K} \)(ω). The element ω is said to be generating for the element φ. A subfield of \( \mathbb{K} \)(x 1,..., x n ) is said to be saturated if, together with every its element, the subfield also contains the generating element. In the paper, the saturation property is studied for the subfields of invariants \( \mathbb{K} \)(x 1,..., x n ) G of a finite group G of automorphisms of the field \( \mathbb{K} \)(x 1..., x n ).

Key words

finite group saturated subfield polynomial ring polynomial invariant subalgebra of invariants closed rational function the groups SL2(ℂ) PSL2(ℂ). 


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Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.Moscow State UniversityMoscowRussia
  2. 2.Kiev National UniversityKievUkraine

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