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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $G$ and $N$ be finite groups of order $2n$ where $n$ is odd. We say thepair $(G,N)$ is Hopf-Galois realizable if $G$ is a regular subgroup of$\h(N)=N\rtimes\au(N)$. In this article we give necessary conditions on $G$(similarly $N$) when $N$ (similarly $G$) is a group of the form$\mathbb{Z}_n\rtimes\mathbb{Z}_2$. Further we show that this condition is alsosufficient if radical of $n$ is a Burnside number. This classifies all the skewbraces which has the additive group (or the multiplicative group) to beisomorphic to $\mathbb{Z}_n\rtimes\mathbb{Z}_2$, in this case.

Hopf-Galois Realizability of $\mathbb{Z}_n\rtimes\mathbb{Z}_2$