English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Let $K$ be any field and $G$ be a finite group. Let $G$ act on the rationalfunction field $K(x_g:g\in G)$ by $K$-automorphisms defined by $g\cdotx_h=x_{gh}$ for any $g,h\in G$. Noether's problem asks whether the fixed field$K(G)=K(x_g:g\in G)^G$ is rational (=purely transcendental) over $K$. We willprove that if $G$ is a non-abelian $p$-group of order $p^n$ ($n\ge 3$)containing a cyclic subgroup of index $p^2$ and $K$ is any field containing aprimitive $p^{n-2}$-th root of unity, then $K(G)$ is rational over $K$. As acorollary, if $G$ is a non-abelian $p$-group of order $p^3$ and $K$ is a fieldcontaining a primitive $p$-th root of unity, then $K(G)$ is rational.

Noether's problem for p_groups with a cyclic subgroup of index p^2