Categories
2020 Projects

Wild Automorphisms of the Complex Field of Finite and Infinite Orders

Elizabeth Wolfe ’21
Majors: Mathematics, English

Elizabeth Wolfe ’21

Majors: Mathematics, English

Faculty Collaborator: Marlow Anderson, Mathematics & Computer Science

Abstract: A wild automorphism is an automorphism of the complex field that does not leave the real numbers fixed, unlike the two ‘classic’ automorphisms of the complex numbers: the identity automorphism and conjugation. In this paper we use Zorn’s Lemma to prove that any automorphism of a subfield of the complex field that has a finite order can be extended to an automorphism of the entire complex field of the same order. It then follows that there exists automorphisms of the complex field of order n for every finite n. Finally, we show that there exists an automorphism of the complex field of infinite order.

Leave a Reply

Your email address will not be published.

css.php