| Title:
|
Exponent of class group of certain imaginary quadratic fields (English) |
| Author:
|
Chakraborty, Kalyan |
| Author:
|
Hoque, Azizul |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
70 |
| Issue:
|
4 |
| Year:
|
2020 |
| Pages:
|
1167-1178 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $n>1$ be an odd integer. We prove that there are infinitely many imaginary quadratic fields of the form $\mathbb {Q} \bigl (\sqrt {x^2-2y^n} \bigr )$ whose ideal class group has an element of order $n$. This family gives a counterexample to a conjecture by H. Wada (1970) on the structure of ideal class groups. (English) |
| Keyword:
|
quadratic field |
| Keyword:
|
discriminant |
| Keyword:
|
class group |
| Keyword:
|
Wada's conjecture |
| MSC:
|
11R11 |
| MSC:
|
11R29 |
| idZBL:
|
07285988 |
| idMR:
|
MR4181805 |
| DOI:
|
10.21136/CMJ.2020.0289-19 |
| . |
| Date available:
|
2020-11-18T09:50:26Z |
| Last updated:
|
2023-01-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148420 |
| . |
| Reference:
|
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| Reference:
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