Reduction theorems for Noether’s problem

DOI10.1090/S0002-9939-09-09608-7zbMath1177.12006arXiv0709.1297OpenAlexW2008939388MaRDI QIDQ3629404

Bernat Plans, Ming-chang Kang

Publication date: 27 May 2009

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0709.1297

zbMATH Keywords

inverse Galois theoryNoether's problemrationality problem

Mathematics Subject Classification ID

Galois theory (11R32) Actions of groups on commutative rings; invariant theory (13A50) Inverse Galois theory (12F12) Transcendental field extensions (12F20) Rationality questions in algebraic geometry (14E08)

Related Items

On Noether's problem for central extensions of symmetric and alternating groups, Noether's Problem for p-Groups with an Abelian Subgroup of Index p, Noether's problem on semidirect product groups, Noether's problem for some semidirect products, Noether's problem for \(p\)-groups with a cyclic subgroup of index \(p^{2}\), Rational invariants for subgroups of \(S_5\) and \(S_7\), Noether's problem for the groups with a cyclic subgroup of index 4, Retract rational fields, Frobenius groups and retract rationality, Noether's problem for some subgroups of \(S_{14}\): the modular case, Noether's problem for groups of order 32, Invariants of wreath products and subgroups of \(S_6\), On Noether's problem for cyclic groups of prime order, Multiplicative Invariant Fields of Dimension ≤6

Cites Work

• Unnamed Item
• Unnamed Item
• Rational invariants of meta-abelian groups of linear automorphisms
• Retract rational fields and cyclic Galois extensions
• Generic Galois extensions and problems in field theory
• Rationality of some projective linear actions
• Some actions of symmetric groups
• Noether's problem for \(\text{GL}(2, 3)\)
• On a Problem of Chevalley