Exponents of class groups of certain imaginary quadratic fields

Kalyan Chakraborty; Azizul Hoque

Exponents of class groups of certain imaginary quadratic fields

Number Theory 2019-09-05 v2

Authors: Kalyan Chakraborty , Azizul Hoque

Abstract

Let $n>1$ be an odd integer. We prove that there are infinitely many imaginary quadratic fields of the form $\mathbb{Q}(\sqrt{x^2-2y^n})$ whose ideal class group has an element of order $n$ . This family gives a counter example to a conjecture by H. Wada \cite{WA70} on the structure of ideal class groups.

Keywords

imaginary quadratic fields ideal class group exponent of class group wada conjecture counter example

Cite

@article{arxiv.1801.00392,
  title  = {Exponents of class groups of certain imaginary quadratic fields},
  author = {Kalyan Chakraborty and Azizul Hoque},
  journal= {arXiv preprint arXiv:1801.00392},
  year   = {2019}
}

Comments

11 pages. To appear in Czechoslovak Mathematical Journal

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