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 $p$.
Publié le : 2001-04-14
Classification:
Cyclic field,
class number,
Frobenius group,
11R29,
11R20,
12F10
@article{1148393081,
author = {Kishi, Yasuhiro},
title = {Imaginary cyclic fields of degree $p - 1$ whose relative class numbers are divisible by $p$},
journal = {Proc. Japan Acad. Ser. A Math. Sci.},
volume = {77},
number = {10},
year = {2001},
pages = { 55-58},
language = {en},
url = {http://dml.mathdoc.fr/item/1148393081}
}
Kishi, Yasuhiro. Imaginary cyclic fields of degree $p - 1$ whose relative class numbers are divisible by $p$. Proc. Japan Acad. Ser. A Math. Sci., Tome 77 (2001) no. 10, pp. 55-58. http://gdmltest.u-ga.fr/item/1148393081/