We prove, for a field $K$ which is cyclic of odd prime powerdegree over the rationals, that the annihilator of thequotient of the units of $K$ by a suitable large subgroup (constructedfrom circular units) annihilates what we call thenon-genus part of the class group.This leads to stronger annihilation results for the wholeclass group than a routine application of the Rubin--Thaine methodwould produce, since thepart of the class group determined by genus theory has an obviouslarge annihilator which is not detected bythat method; this is our reason for concentrating onthe non-genus part. The present work builds on and strengthensprevious work of the authors; the proofs are more conceptual now,and we are also able to construct an example which demonstratesthat our results cannot be easily sharpened further.
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机译：我们证明，对于在奇数上有奇次幂次幂而在有理数上循环的字段$ K $，由适当的大子组（由圆形单位构成）的$ K $单位商的the灭子会消灭我们称为非属的部分这将导致整个班级的歼灭效果比常规应用鲁宾-桑因方法产生的歼灭效果更好，因为由属理论确定的班级部分中有一个明显的大型歼灭者，而该方法没有检测到该歼灭者。这是我们专注于非属部分的原因。本工作建立在并加强了作者先前的工作之上;现在，证明更加概念化了，我们还可以构建一个例子，说明我们的结果不能轻易得到进一步完善。
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