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On the structure of Galois groups of tamely ramified pro-p extensions of imaginary quadratic fields.

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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]
Copyright of Journal of Number Theory is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 193886682
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PubType: Academic Journal
PubTypeId: academicJournal
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  Data: On the structure of Galois groups of tamely ramified pro-p extensions of imaginary quadratic fields.
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  Data: <searchLink fieldCode="AR" term="%22Liu%2C+Qi%22">Liu, Qi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> QiLiu67@aliyun.com</i><br /><searchLink fieldCode="AR" term="%22Xing%2C+Zugan%22">Xing, Zugan</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> xingzugan@aliyun.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Number+Theory%22">Journal of Number Theory</searchLink>. Oct2026, Vol. 287, p136-153. 18p.
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  Data: <searchLink fieldCode="DE" term="%22Galois+theory%22">Galois theory</searchLink><br /><searchLink fieldCode="DE" term="%22Quadratic+fields%22">Quadratic fields</searchLink><br /><searchLink fieldCode="DE" term="%22Irreducible+polynomials%22">Irreducible polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Field+extensions+%28Mathematics%29%22">Field extensions (Mathematics)</searchLink>
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  Data: 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]
– Name: AbstractSuppliedCopyright
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  Group: Ab
  Data: <i>Copyright of Journal of Number Theory is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1016/j.jnt.2025.07.019
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 18
        StartPage: 136
    Subjects:
      – SubjectFull: Galois theory
        Type: general
      – SubjectFull: Quadratic fields
        Type: general
      – SubjectFull: Irreducible polynomials
        Type: general
      – SubjectFull: Field extensions (Mathematics)
        Type: general
    Titles:
      – TitleFull: On the structure of Galois groups of tamely ramified pro-p extensions of imaginary quadratic fields.
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          Name:
            NameFull: Liu, Qi
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            NameFull: Xing, Zugan
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          Dates:
            – D: 01
              M: 10
              Text: Oct2026
              Type: published
              Y: 2026
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              Value: 287
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            – TitleFull: Journal of Number Theory
              Type: main
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