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- W4280495319 abstract "Let $p$ be an odd prime number and let $2^{e+1}$ be the highest power of 2 dividing $p - 1$. For $0 leq n leq e$, let $k_{n}$ be the real cyclic field of conductor $p$ and degree $2^{n}$. For a certain imaginary quadratic field $L_{0}$, we put $L_{n} = L_{0} k_{n}$. For $0 leq n leq e - 1$, let $mathcal{F}_{n}$ be the imaginary quadratic subextension of the imaginary $(2, 2)$-extension $L_{n+1}/k_{n}$ with $mathcal{F}_{n} neq L_{n}$. We study the Galois module structure of the 2-part of the ideal class group of the imaginary cyclic field $mathcal{F}_{n}$. This generalizes a classical result of Rédei and Reichardt for the case $n = 0$." @default.
- W4280495319 created "2022-05-22" @default.
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- W4280495319 date "2022-07-22" @default.
- W4280495319 modified "2023-10-18" @default.
- W4280495319 title "On the class groups of certain imaginary cyclic fields of 2-power degree" @default.
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- W4280495319 doi "https://doi.org/10.2969/jmsj/86438643" @default.
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