## Nihonkai Mathematical Journal

- Nihonkai Math. J.
- Volume 28, Number 2 (2017), 99-104.

### A note on Galois embedding and its application to $\mathbb P^n$

#### Abstract

We show a condition that a Galois covering $\pi : V \longrightarrow \mathbb P^n$ is induced by a Galois embedding. Then we consider the Galois embedding for $\mathbb P^n$. If the Galois group $G$ is abelian, then $G \cong \bigoplus\limits^{n} Z_d$ and the projection $\pi$ can be expressed as $\pi(X_0:X_1: \cdots :X_n)=({X_0}^d:{X_1}^d:\cdots:{X_n}^d)$.

#### Note

This work is based on research 15K04813 supported by Grant-in-Aid for Scientific Research (C) from Japan Society for the Promotion of Science.

#### Article information

**Source**

Nihonkai Math. J., Volume 28, Number 2 (2017), 99-104.

**Dates**

Received: 22 September 2016

Revised: 13 May 2017

First available in Project Euclid: 26 April 2018

**Permanent link to this document**

https://projecteuclid.org/euclid.nihmj/1524708084

**Mathematical Reviews number (MathSciNet)**

MR3794318

**Zentralblatt MATH identifier**

06873762

**Subjects**

Primary: 14N05: Projective techniques [See also 51N35] 14N10: Enumerative problems (combinatorial problems)

Secondary: 14J99: None of the above, but in this section

**Keywords**

Galois embedding Galois group projective space

#### Citation

Yoshihara, Hisao. A note on Galois embedding and its application to $\mathbb P^n$. Nihonkai Math. J. 28 (2017), no. 2, 99--104. https://projecteuclid.org/euclid.nihmj/1524708084