Degree 12 2-adic fields with automorphism group of order 4

Abstract

This paper is concerned with the 513 isomorphism classes of degree~12 2-adic fields whose automorphism groups have order~4. For each extension, we identify a defining polynomial, the extension's ramification index, residue degree, discriminant, and the Galois group of the extension's normal closure. These results extend previous work of Jones and Roberts, Awtrey and Shill.