Bibliographic Details
| Title: |
On the structure of Galois groups of tamely ramified pro-p extensions of imaginary quadratic fields. |
| Authors: |
Liu, Qi1 (AUTHOR) QiLiu67@aliyun.com, Xing, Zugan1,2 (AUTHOR) xingzugan@aliyun.com |
| Source: |
Journal of Number Theory. Oct2026, Vol. 287, p136-153. 18p. |
| Subjects: |
Galois theory, Quadratic fields, Irreducible polynomials, Field extensions (Mathematics) |
| Abstract: |
For a prime p , we study the Galois groups of maximal pro- p extensions of imaginary quadratic fields unramified outside a finite set S consisting of one or two finite places not lying above p. Our main theoretical result provides explicit presentations for these Galois groups under certain conditions. As an application, we provide an example of the maximal pro-2 extension of Q (− 3) unramified outside three specific finite places, whose Galois group is isomorphic to the quaternion group Q 8 , and determine the defining polynomial of the maximal pro-3 extension of Q (i) unramified outside two specific finite places. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
