Proceedings of the Japan Academy, Series A, Mathematical Sciences

Imaginary cyclic fields of degree $p - 1$ whose relative class numbers are divisible by $p$

Yasuhiro Kishi

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We give a sufficient condition for an imaginary cyclic field of degree $p - 1$ containing $\mathbf{Q}(\zeta + \zeta^{-1})$ to have the relative class number divisible by $p$. As a consequence, we see that there exist infinitely many imaginary cyclic fields of degree $p - 1$ with the relative class number divisible by $p$.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 77, Number 4 (2001), 55-58.

First available in Project Euclid: 23 May 2006

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Zentralblatt MATH identifier

Primary: 11R29: Class numbers, class groups, discriminants
Secondary: 11R20: Other abelian and metabelian extensions 12F10: Separable extensions, Galois theory

Cyclic field class number Frobenius group


Kishi, Yasuhiro. Imaginary cyclic fields of degree $p - 1$ whose relative class numbers are divisible by $p$. Proc. Japan Acad. Ser. A Math. Sci. 77 (2001), no. 4, 55--58. doi:10.3792/pjaa.77.55.

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