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Invariant part of class groups and distribution of relative class group.

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Title: Invariant part of class groups and distribution of relative class group.
Authors: Wang, Weitong1 (AUTHOR) 93thomaswang@gmail.com
Source: Journal of Number Theory. Feb2026, Vol. 279, p691-748. 58p.
Subjects: Class groups (Mathematics), Sylow subgroups, Group extensions (Mathematics), Field extensions (Mathematics), Mathematical analysis, Number theory
Abstract: We generalize the work of Roquette and Zassenhaus on the invariant part of the class groups to the relative class groups. Thus, we can show some statistical results as follows. For abelian extensions over a fixed number field K , we show infinite C p -moments for the Sylow p -subgroup of the relative class group when p divides the degree of the extension. For sextic number fields with A 4 -closure, we can show infinite C 2 -moments for the Sylow 2-subgroup of the relative class group when the extensions run over a fixed Galois cubic field. • Prove infinite moments of relative class groups for bad primes in Cohen-Lenstra Heuristics. • Non-randomness of class groups in certain non-abelian extensions. • Estimate of field-counting which generalizes the case of nowhere totally ramified cubic fields. • Results related to ambiguous class groups that generalizes the work of Roquette and Zassenhauss. • Generalized discriminant that is applied to the study of distribution of class groups. [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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  Data: Invariant part of class groups and distribution of relative class group.
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  Data: <searchLink fieldCode="AR" term="%22Wang%2C+Weitong%22">Wang, Weitong</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> 93thomaswang@gmail.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Number+Theory%22">Journal of Number Theory</searchLink>. Feb2026, Vol. 279, p691-748. 58p.
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  Data: <searchLink fieldCode="DE" term="%22Class+groups+%28Mathematics%29%22">Class groups (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Sylow+subgroups%22">Sylow subgroups</searchLink><br /><searchLink fieldCode="DE" term="%22Group+extensions+%28Mathematics%29%22">Group extensions (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Field+extensions+%28Mathematics%29%22">Field extensions (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Number+theory%22">Number theory</searchLink>
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  Data: We generalize the work of Roquette and Zassenhaus on the invariant part of the class groups to the relative class groups. Thus, we can show some statistical results as follows. For abelian extensions over a fixed number field K , we show infinite C p -moments for the Sylow p -subgroup of the relative class group when p divides the degree of the extension. For sextic number fields with A 4 -closure, we can show infinite C 2 -moments for the Sylow 2-subgroup of the relative class group when the extensions run over a fixed Galois cubic field. • Prove infinite moments of relative class groups for bad primes in Cohen-Lenstra Heuristics. • Non-randomness of class groups in certain non-abelian extensions. • Estimate of field-counting which generalizes the case of nowhere totally ramified cubic fields. • Results related to ambiguous class groups that generalizes the work of Roquette and Zassenhauss. • Generalized discriminant that is applied to the study of distribution of class groups. [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:
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      – Type: doi
        Value: 10.1016/j.jnt.2025.07.012
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 58
        StartPage: 691
    Subjects:
      – SubjectFull: Class groups (Mathematics)
        Type: general
      – SubjectFull: Sylow subgroups
        Type: general
      – SubjectFull: Group extensions (Mathematics)
        Type: general
      – SubjectFull: Field extensions (Mathematics)
        Type: general
      – SubjectFull: Mathematical analysis
        Type: general
      – SubjectFull: Number theory
        Type: general
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      – TitleFull: Invariant part of class groups and distribution of relative class group.
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              Text: Feb2026
              Type: published
              Y: 2026
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              Value: 279
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            – TitleFull: Journal of Number Theory
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