Some Remarks on the Divisibility of the Class Numbers of Imaginary Quadratic Fields

Some Remarks on the Divisibility of the Class Numbers of Imaginary Quadratic Fields

For a given integer <i>n</i>, we provide some families of imaginary quadratic number fields of the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="double-struck&qu...

Full description

Bibliographic Details
Main Author: Kwang-Seob Kim
Format: Article
Language:English
Published: MDPI AG 2022-07-01
Series:Mathematics
Subjects:
class number
imaginary quadratic fields
divisibility of class number
Online Access:https://www.mdpi.com/2227-7390/10/14/2488
Description
Summary:For a given integer <i>n</i>, we provide some families of imaginary quadratic number fields of the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="double-struck">Q</mi><mo>(</mo><msqrt><mrow><mn>4</mn><msup><mi>q</mi><mn>2</mn></msup><mo>−</mo><msup><mi>p</mi><mi>n</mi></msup></mrow></msqrt><mo>)</mo></mrow></semantics></math></inline-formula>, whose ideal class group has a subgroup isomorphic to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="double-struck">Z</mi><mo>/</mo><mi>n</mi><mi mathvariant="double-struck">Z</mi></mrow></semantics></math></inline-formula>.
ISSN:2227-7390

Similar Items