Primary components of the ideal class group of the $\mathbf{Z}_p$-extension over $\mathbf{Q}$ for typical inert primes
Horie, Kuniaki
Proc. Japan Acad. Ser. A Math. Sci., Tome 81 (2005) no. 3, p. 40-43 / Harvested from Project Euclid
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Let $p$ be an odd prime, $\mathbf Z_p$ the ring of $p$-adic integers, and $l$ a prime number different from $p$. We have shown in [1] that, if $l$ is a sufficiently large primitive root modulo $p^2$, then the $l$-class group of the $\mathbf Z_p$-extension over the rational field is trivial. We shall modify part of the proof of the above result and see, in the case $p\leq 7$, that the result holds without assuming $l$ to be sufficiently large.
Publié le : 2005-03-14
Classification:  $\mathbf Z_p$-extension,  ideal class group,  11R20,  11R23,  11R29 
@article{1116442034,
     author = {Horie, Kuniaki},
     title = {Primary components of the ideal class group of the $\mathbf{Z}\_p$-extension
 over $\mathbf{Q}$ for typical inert primes},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {81},
     number = {3},
     year = {2005},
     pages = { 40-43},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1116442034}
}

Horie, Kuniaki. Primary components of the ideal class group of the $\mathbf{Z}_p$-extension
 over $\mathbf{Q}$ for typical inert primes. Proc. Japan Acad. Ser. A Math. Sci., Tome 81 (2005) no. 3, pp.  40-43. http://gdmltest.u-ga.fr/item/1116442034/