Let [Formula: see text] be the minus quotient of the ideal class group of the [Formula: see text]th cyclotomic field. In this paper, first, we show that each finite abelian group appears as a subgroup of [Formula: see text] for some [Formula: see text]. Second, we show that, for all pairs of integers [Formula: see text] and [Formula: see text] with [Formula: see text], the kernel of the lifting map [Formula: see text] is contained in the [Formula: see text]-torsion [Formula: see text] of [Formula: see text]. Such an evaluation of the exponent is an individuality of cyclotomic fields.

中文翻译：

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关于分圆场理想类群的负商

令 [Formula: see text] 为第 [Formula: see text] 分圆域的理想类群的负商。在本文中，首先，我们证明每个有限阿贝尔群对于某些 [公式：参见文本] 表现为 [公式：参见文本] 的子群。其次，我们证明，对于所有整数对 [Formula: see text] 和 [Formula: see text] 与 [Formula: see text]，提升图 [Formula: see text] 的内核包含在 [Formula ：见正文]-扭力[公式：见正文]的[公式：见正文]。指数的这种评估是分圆场的个体性。