Zur Bestimmung der metazyklischen Minimalbasis von Primzahlgrad

Breuer, Sebastian

doi:10.1007/bf01448438

Search citation statements

Order By: Relevance

Paper Sections

Select...

§1 Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

1934

2013

Publication Types

Select...

Article2

Other1

Relationship

Self Cite0

Independent3

Authors

Journals

Cited by 3 publications

(1 citation statement)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the other hand only a handful of results for the rationality of Q(G) were known before 1950's. Samson Breuer was able to show that Q(Z 3 ) and Q(Z 6 ) are rational over Q where Z n is the cyclic group of order n [Br1]; he then showed that Q(G) is rational for some transitive solvable subgroup G contained in S p , the symmetric group of degree p, if p = 5 or 7 [Br2]. Breuer's results for transitive solvable subgroups in S p was extended by Furtwängler for p = 5,7,11 [Fr]; finally Breuer himself extended these results for any prime number p ≤ 23 [Br3].…”

Section: §1 Introductionmentioning

confidence: 99%

Action of dihedral groups

Kang

2013

Preprint

View full text Add to dashboard Cite

Let K be any field and G be a finite group. Let G act on the rational function field K(x g : g ∈ G) by K-automorphisms defined by g • x h = x gh for any g, h ∈ G. Denote by K(G) the fixed field K(x g : g ∈ G) G . Noether's problem asks whether K(G) is rational (=purely transcendental) over K. We will give a brief survey of Noether's problem for abelian groups and dihedral groups, and will show that Q(D n ) is rational over Q for n ≤ 10.

show abstract

Section: §1 Introductionmentioning

confidence: 99%