On a Theorem of Kawamoto on Normal Bases of Rings of Integers, II

[摘要] Let $m=p^e$ be a power of a prime number $p$.We say that a number field $F$ satisfies the property $(H_m')$when for any $a in F^{imes}$, the cyclic extension$F(z_m, a^{1/m})/F(z_m)$ has a normal $p$-integral basis.We prove that $F$ satisfies $(H_m')$if and only if the natural homomorphism $Cl_F' o Cl_K'$ is trivial.Here $K=F(zeta_m)$, and $Cl_F'$ denotes the ideal class group of $F$with respect to the $p$-integer ring of $F$.

[学科分类] 数学（综合）

[关键词] Quotients;involutions;real forms;Lagrangian loci