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NOTE ON THE p-DIVISIBILITY OF CLASS NUMBERS OF AN INFINITE FAMILY OF IMAGINARY QUADRATIC FIELDS

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  20 May 2021

SRIlAKSHMI KRISHNAMOORTHY  and
SUNIL KUMAR PASUPULATI
SRIlAKSHMI KRISHNAMOORTHY
Affiliation:
Indian Institute of Science Education and Research, Thiruvananthapuram, India e-mails: [email protected]; [email protected]
SUNIL KUMAR PASUPULATI
Affiliation:
Indian Institute of Science Education and Research, Thiruvananthapuram, India e-mails: [email protected]; [email protected]
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Abstract

For any odd prime p, we construct an infinite family of imaginary quadratic fields whose class numbers are divisible by p. We give a corollary that settles Iizuka’s conjecture for the case n=1 and p>2.

MSC classification

Primary: 11R29: Class numbers, class groups, discriminants
Secondary: 11R11: Quadratic extensions
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 64 , Issue 2 , May 2022 , pp. 352 - 357
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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