The narrow class groups of the ℤ17- and ℤ19-extensions over the rational field
The narrow class groups of the ℤ17- and ℤ19-extensions over the rational field
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有理域上 ℤ17- 和 ℤ19- 扩展的狭义类群
DOI：
10.1007/s12188-009-0030-3
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
M. Horie
中科院分区：
文献类型：
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作者：
K. Horie;M. Horie
设为17或19，设ℤP表示p进整数环，设L是一个素数，它是模2的本原根。我们将借助计算机证明有理数域上ℤp-扩张的l-类群是平凡的。我们还将证明相同ℤp-扩张的窄2-类群的平凡性质。
Letpbe either 17 or 19, let ℤpdenote the ring ofp-adic integers, and letlbe a prime number which is a primitive root modulop2. We shall prove, with the help of a computer, that thel-class group of the ℤp-extension over the rational field is trivial. We shall also prove the triviality of the narrow 2-class group of the same ℤp-extension.