Rationality of some projective linear actions

DOI10.1006/jabr.2000.8292zbMath0993.12003OpenAlexW2047795913MaRDI QIDQ1570370

Hamza Ahmad, Mowaffaq Hajja, Ming-chang Kang

Publication date: 18 November 2001

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.2000.8292

zbMATH Keywords

group actionsrationalityfixed subfields

Mathematics Subject Classification ID

Transcendental field extensions (12F20) Field extensions (12F99)

Related Items (33)

Noether’s Problem for Some p-Groups ⋮ Bogomolov multipliers for some \(p\)-groups of nilpotency class 2 ⋮ Rationality problem for transitive subgroups of \(S_8\) ⋮ Noether's Problem for p-Groups with an Abelian Subgroup of Index p ⋮ Fixed fields of triangular matrix groups ⋮ Noether's problem on semidirect product groups ⋮ Negligibility of projective linear automorphisms ⋮ Three-dimensional purely quasimonomial actions ⋮ Noether's problem for \(p\)-groups with a cyclic subgroup of index \(p^{2}\) ⋮ Rationality of three-dimensional quotients by monomial actions ⋮ Birational classification of fields of invariants for groups of order 128 ⋮ Rational invariants for subgroups of \(S_5\) and \(S_7\) ⋮ Noether's problem for the groups with a cyclic subgroup of index 4 ⋮ The rationality problem for finite subgroups of \(\mathrm{GL}_4(\mathbb Q)\) ⋮ Frobenius groups and retract rationality ⋮ Rationality of the quotient of \(\mathbb P^2\) by finite group of automorphisms over arbitrary field of characteristic zero ⋮ Rationality problem of \(GL_{4}\) group actions. ⋮ Noether's problem for some subgroups of \(S_{14}\): the modular case ⋮ Rationality problem of three-dimensional monomial group actions ⋮ Noether's problem for groups of order 243 ⋮ Relative negligibility of linear automorphisms ⋮ Noether's problem for groups of order 32 ⋮ Noether's problem for \(\text{GL}(2, 3)\) ⋮ Rationality problem of three-dimensional purely monomial group actions: the last case ⋮ Rationality of \(P\)-group actions ⋮ Noether's problem for metacyclic \(p\)-groups ⋮ Some group actions on \(K(x_1,x_2,x_3)\) ⋮ Noether's problem for four- and five-dimensional linear actions ⋮ Rationality problem for some meta-abelian groups ⋮ Reduction theorems for Noether’s problem ⋮ Rationality problem for some transitive subgroups of S₁₄ ⋮ THE RATIONALITY PROBLEM FOR THREE- AND FOUR-DIMENSIONAL PERMUTATIONAL GROUP ACTIONS ⋮ Invariants of wreath products and subgroups of \(S_6\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Rationality of the field of invariants of a triangular group
• On Castelnuovo's criterion of rationality P\(_a\)=P\(_2\)=0 of an algebraic surface
• On subfields of rational function fields
• Noether's problem over an algebraically closed field
• Rationality of finite groups of monomial automorphisms of k(x,y)
• Finite group actions on rational function fields
• Rational functions invariant under a finite Abelian group
• Negligibility of projective linear automorphisms
• Some actions of symmetric groups
• Invariant rational functions and a problem of Steenrod
• Invariants of finite Abelian groups
• RATIONALITY OF FIELDS OF INVARIANTS OF SOME FOUR-DIMENSIONAL LINEAR GROUPS, AND AN EQUIVARIANT CONSTRUCTION RELATED TO THE SEGRE CUBIC
• A note on affine automorphisms
• ON TWO-DIMENSIONAL ALGEBRAIC TORI. II
• Invariants of Certain Groups I
• ON THE QUESTION OF THE STRUCTURE OF THE SUBFIELD OF INVARIANTS OF A CYCLIC GROUP OF AUTOMORPHISMS OF THE FIELDQ(x₁,...,x_n)

This page was built for publication: Rationality of some projective linear actions