Abstract
Let $p$ be a prime number. A number field $F$ satisfies the condition $(H_p)$ when any tame cyclic extention $N/F$ of degree $p$ has a normal integral basis. For the case $p=2$, it is shown by Mann that $F$ satisfies $(H_2)$ only when $h_F=1$ where $h_F$ is the class number of $F$. We prove that if an imaginary quadratic field $F$ satisfies $(H_p)$ for some $p$, then $h_F=1$.
Citation
Humio Ichimura. "Note on imaginary quadratic fields satisfying the Hilbert-Speiser condition at a prime p." Proc. Japan Acad. Ser. A Math. Sci. 83 (6) 88 - 91, June 2007. https://doi.org/10.3792/pjaa.83.88
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