Ramified at 3 Totally Real Cubic Galois Field

Student: Elena Kukhtina

Educational Programme: Joint Bachelor's Programme with the Centre for Teaching Excellence (Bachelor)

Year of Graduation: 2024

Galois theory was introduced for the first time by Evariste Galois in the 19th century. He laid the foundation for the theory of groups and fields. Galois theory is based on the definition of Galois extension and Galois groups. In this paper, I will consider a field that is obtained by attaching the roots of an explicit cubic equation, which is a Galois extension. During the course of my work, I will describe the maximum order of this field as well as the groups of invertible elements in it.

Student Theses at HSE must be completed in accordance with the University Rules and regulations specified by each educational programme.

Summaries of all theses must be published and made freely available on the HSE website.

The full text of a thesis can be published in open access on the HSE website only if the authoring student (copyright holder) agrees, or, if the thesis was written by a team of students, if all the co-authors (copyright holders) agree. After a thesis is published on the HSE website, it obtains the status of an online publication.

Student theses are objects of copyright and their use is subject to limitations in accordance with the Russian Federation’s law on intellectual property.

In the event that a thesis is quoted or otherwise used, reference to the author’s name and the source of quotation is required.

Search all student theses