Exponents of class groups of certain imaginary quadratic fields

2018/01/01 by Chakraborty, Kalyan, Hoque, Azizul
#11R11 #11R29 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1801.00392

Abstract

Let n>1 be an odd integer. We prove that there are infinitely many imaginary quadratic fields of the form ℚ(√(x²-2yⁿ)) whose ideal class group has an element of order n. This family gives a counter example to a conjecture by H. Wada \citeWA70 on the structure of ideal class groups.

Related

• On the exponents of class groups of some families of imaginary quadratic fields
• Divisibility of the class numbers of imaginary quadratic fields
• Class groups of imaginary quadratic fields of 3-rank at least 2
• Imaginary quadratic number fields with class groups of small exponent
• Divisibility of class numbers of quadratic fields and a conjecture of Iizuka