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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/14/2488 |
| _version_ | 1797445394422038528 |
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| author | Kwang-Seob Kim |
| author_facet | Kwang-Seob Kim |
| author_sort | Kwang-Seob Kim |
| collection | DOAJ |
| description | 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>. |
| first_indexed | 2024-03-09T13:26:09Z |
| format | Article |
| id | doaj.art-4947eee1b75a4c7d89cee2e597706cea |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T13:26:09Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-4947eee1b75a4c7d89cee2e597706cea2023-11-30T21:24:04ZengMDPI AGMathematics2227-73902022-07-011014248810.3390/math10142488Some Remarks on the Divisibility of the Class Numbers of Imaginary Quadratic FieldsKwang-Seob Kim0Department of Mathematics, Chosun University, 309 Pilmundaero, Gwangju 61452, KoreaFor 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>.https://www.mdpi.com/2227-7390/10/14/2488class numberimaginary quadratic fieldsdivisibility of class number |
| spellingShingle | Kwang-Seob Kim Some Remarks on the Divisibility of the Class Numbers of Imaginary Quadratic Fields Mathematics class number imaginary quadratic fields divisibility of class number |
| title | Some Remarks on the Divisibility of the Class Numbers of Imaginary Quadratic Fields |
| title_full | Some Remarks on the Divisibility of the Class Numbers of Imaginary Quadratic Fields |
| title_fullStr | Some Remarks on the Divisibility of the Class Numbers of Imaginary Quadratic Fields |
| title_full_unstemmed | Some Remarks on the Divisibility of the Class Numbers of Imaginary Quadratic Fields |
| title_short | Some Remarks on the Divisibility of the Class Numbers of Imaginary Quadratic Fields |
| title_sort | some remarks on the divisibility of the class numbers of imaginary quadratic fields |
| topic | class number imaginary quadratic fields divisibility of class number |
| url | https://www.mdpi.com/2227-7390/10/14/2488 |
| work_keys_str_mv | AT kwangseobkim someremarksonthedivisibilityoftheclassnumbersofimaginaryquadraticfields |