Note on imaginary quadratic fields satisfying the Hilbert-Speiser condition at a prime p
Ichimura, Humio
Proc. Japan Acad. Ser. A Math. Sci., Tome 83 (2007) no. 1, p. 88-91 / Harvested from Project Euclid
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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 $h_F=1$.
Publié le : 2007-06-14
Classification:  Hilbert-Speiser number field,  imaginary quadratic field,  11R33,  11R11 
@article{1188405577,
     author = {Ichimura, Humio},
     title = {Note on imaginary quadratic fields satisfying the Hilbert-Speiser condition at a prime p},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {83},
     number = {1},
     year = {2007},
     pages = { 88-91},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1188405577}
}

Ichimura, Humio. Note on imaginary quadratic fields satisfying the Hilbert-Speiser condition at a prime p. Proc. Japan Acad. Ser. A Math. Sci., Tome 83 (2007) no. 1, pp.  88-91. http://gdmltest.u-ga.fr/item/1188405577/