%0 Journal Article %A Kuniaki Horie %A Mitsuko Horie %T The narrow class groups of some $\mathbb Z_p$-extensions over the rationals %J Acta Arithmetica %D 2008 %P 159-180 %V 135 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/aa135-2-5/ %R 10.4064/aa135-2-5 %G en %F 10_4064_aa135_2_5