Invariant rational functions and a problem of Steenrod

  title={Invariant rational functions and a problem of Steenrod},
  author={Richard G. Swan},
  journal={Inventiones mathematicae},
  • R. Swan
  • Published 1969
  • Mathematics
  • Inventiones mathematicae
This is an expository paper on work of Endo and Miyata which leads to a computation of the flabby class group of a finite cyclic group.
Real Quantifier Elimination in Practice
A survey over the knowledge on some structural properties of such rings and fields of invariants as polynomials and rational functions which are invariant under the action of a finite linear group. Expand
Birational invariants of crystals and fields with a finite group of operators
It is well known that an n -dimensional crystallographic group can be reconstructed from its point group, the integral representation of the point group which arises from its action on theExpand
A note on monomial automorphisms
Abstract Previous results (Hajja, J. Algebra73 (1981), 30–36) on monomial automorphisms are strengthened and the rationality of all monomial automorphisms on k(x,y) is established. The relation ofExpand
Polynomials with Dp as Galois group
Abstract A useful criterion characterizing a monic irreducible polynomial over Q with Galois group Dp (the dihedral group of order 2p, p: prime) is given by making use of the geometry of Dp, i.e., DpExpand
A solution of a problem of Steenrod for cyclic groups of prime order
Given a Z[G] module A, we will say a simply connected CW complex X is of type (A, n) if X admits a cellular G action, and Hi(X) = 0, i # n, H,,(X) A as Z[G] modules. In [5], R. Swan considers theExpand
Noether's problem and descent
We study Noether's problem from the perspective of torsors under linear algebraic groups and descent.
The center of the ring of 3×3 generic matrices
Following Procesi, the center of the division ring of generic matrices over a field F is described as the fixed field of the symmetric group acting on a purely transcendental extension of F. For 3×3Expand


Representation theory of finite groups and associated algebras
A loom sley capable of use in high speed looms comprises a substantially tubular member, said tubular member having attached thereto a race board plate and a reed support device, said race boardExpand
Periodic Resolutions for Finite Groups
In 113] I indicated a proof of the following theorem: THEOREM A. Let w be a finite group of order n. Let d be the greatest common divisor of n and p(n), p being Euler's p-function. Suppose 7r hasExpand
The Grothendieck ring of a finite group
IF E is any additive category, the Grothendieck group Kc%?) is defined to be the group with one generator [A] for each object A of V and relations [A] = [A’] + [A”] whenever there is an exactExpand
Modules projectifs et espaces fibrés à fibre vectorielle
© Séminaire Dubreil. Algèbre et théorie des nombres (Secrétariat mathématique, Paris), 1957-1958, tous droits réservés. L’accès aux archives de la collection « Séminaire Dubreil. Algèbre et théorieExpand
On a problem of Chevalley
Recently Prof. Chevalley in Nagoya suggested to the author the following problem: Let k be a field, K 5 = k ( x 1 , x 2 , x 3 , x 4 , x 5 ) be a purely transcendental extension field (ofExpand
Sur les anneaux factoriels
© Bulletin de la S. M. F., 1961, tous droits réservés. L’accès aux archives de la revue « Bulletin de la S. M. F. » (http: // implique l’accordExpand
Induced Representations and Projective Modules