Number Theory Commons^™

Galois 2-Extensions, Masoud Ataei Jaliseh

Electronic Thesis and Dissertation Repository

The inverse Galois problem is a major question in mathematics. For a given base field and a given finite group $G$, one would like to list all Galois extensions $L/F$ such that the Galois group of $L/F$ is $G$.

In this work we shall solve this problem for all fields $F$, and for group $G$ of unipotent $4 \times 4$ matrices over $\mathbb{F}_2$. We also list all $16$ $U_4 (\mathbb{F}_2)$-extensions of $\mathbb{Q}_2$. The importance of these results is that they answer the inverse Galois problem in some specific cases.

This is joint work with J\'an Min\'a\v{c} and Nguyen Duy T\^an.