JOURNAL ARTICLE

Determination of all imaginary cyclic quartic fields of prime class number p≡3(mod4), and non-divisibility of class numbers.

  • Published In: International Journal of Number Theory, 2024, v. 20, n. 3. P. 811 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Ram, Mahesh Kumar 3 of 3

Abstract

Let p be a prime such that p ≡ 3 (mod 4). Then, we show that there is no imaginary cyclic quartic extension K of ℚ whose class number is p. Suppose L / ℚ is a cyclic extension of number fields with an odd degree. Then, we show that 2 does not divide the class number of L if the class group of L is cyclic. We also construct some families of number fields whose class number is not divisible by a fixed prime. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:International Journal of Number Theory. 2024/04, Vol. 20, Issue 3, p811
  • Document Type:Article
  • Subject Area:Science
  • Publication Date:2024
  • ISSN:1793-0421
  • DOI:10.1142/S1793042124500416
  • Accession Number:176852206
  • Copyright Statement:Copyright of International Journal of Number Theory is the property of World Scientific Publishing Company 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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