On the exponents of class groups of some families of imaginary quadratic fields

2020/05/26 by Hoque, Azizul · 1 citation
#11R11 #11R29 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2005.12512

Abstract

Let a≥ 1 and n>1 be odd integers. For a given prime p, we prove under certain conditions that the class groups of imaginary quadratic fields ℚ(√(a²-4pⁿ)) have a subgroup isomorphic to ℤ/nℤ. We also show that this family of fields has infinitely many members with the property that their class groups have a subgroup isomorphic to ℤ/nℤ. In addition, we deduce some unconditional results concerning the divisibility of the class numbers of certain imaginary quadratic fields. At the end, we provide some numerical examples to verify our results.

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• On the simultaneous 3-divisibility of class numbers of quadruples of real quadratic fields

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