Rationality problem for transitive subgroups of S8

Baoshan Wang; Jian Zhou

doi:10.1016/j.jalgebra.2018.10.013

Rationality problem for transitive subgroups of S₈

Baoshan Wang
, Jian Zhou^*

^*Corresponding author for this work

School of Mathematical Sciences

Peking University

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

For any field K and any transitive subgroup G of S₈, let G act naturally on K(x₁,…,x₈) by permuting the variables. We prove that under some minor conditions K(x₁,…,x₈)^G is always K-rational except G is A₈ or G is isomorphic to PGL(2,7). We pay special attentions on the characteristic 2 cases.

Original language	English
Pages (from-to)	272-303
Number of pages	32
Journal	Journal of Algebra
Volume	518
DOIs	https://doi.org/10.1016/j.jalgebra.2018.10.013
State	Published - 15 Jan 2019

Keywords

Noether's problem
Rationality
Symmetric group

Access to Document

10.1016/j.jalgebra.2018.10.013

Cite this

@article{dd72fc1822004b79aa5b03f2bd409207,

title = "Rationality problem for transitive subgroups of S8 ",

abstract = "For any field K and any transitive subgroup G of S8, let G act naturally on K(x1,…,x8) by permuting the variables. We prove that under some minor conditions K(x1,…,x8)G is always K-rational except G is A8 or G is isomorphic to PGL(2,7). We pay special attentions on the characteristic 2 cases.",

keywords = "Noether's problem, Rationality, Symmetric group",

author = "Baoshan Wang and Jian Zhou",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2019",

month = jan,

day = "15",

doi = "10.1016/j.jalgebra.2018.10.013",

language = "英语",

volume = "518",

pages = "272--303",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Rationality problem for transitive subgroups of S8

AU - Wang, Baoshan

AU - Zhou, Jian

PY - 2019/1/15

Y1 - 2019/1/15

N2 - For any field K and any transitive subgroup G of S8, let G act naturally on K(x1,…,x8) by permuting the variables. We prove that under some minor conditions K(x1,…,x8)G is always K-rational except G is A8 or G is isomorphic to PGL(2,7). We pay special attentions on the characteristic 2 cases.

AB - For any field K and any transitive subgroup G of S8, let G act naturally on K(x1,…,x8) by permuting the variables. We prove that under some minor conditions K(x1,…,x8)G is always K-rational except G is A8 or G is isomorphic to PGL(2,7). We pay special attentions on the characteristic 2 cases.

KW - Noether's problem

KW - Rationality

KW - Symmetric group

UR - https://www.scopus.com/pages/publications/85055747749

U2 - 10.1016/j.jalgebra.2018.10.013

DO - 10.1016/j.jalgebra.2018.10.013

M3 - 文章

AN - SCOPUS:85055747749

SN - 0021-8693

VL - 518

SP - 272

EP - 303

JO - Journal of Algebra

JF - Journal of Algebra