Abstract
We prove a general stability theorem for p-class groups of number fields along relative cyclic extensions of degree \(p^2\), which is a generalization of a finite-extension version of Fukuda’s theorem by Li, Ouyang, Xu, and Zhang. As an application, we give an example of a pseudo-null Iwasawa module over a certain 2-adic Lie extension.
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Acknowledgements
The authors thank the referee for careful reading and helpful comments for the improvement of this paper. This work was partially supported by JSPS KAKENHI Grant No. JP17K05167.
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Mizusawa, Y., Yamamoto, K. On p-class groups of relative cyclic p-extensions. Arch. Math. 117, 253–260 (2021). https://doi.org/10.1007/s00013-021-01619-8
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DOI: https://doi.org/10.1007/s00013-021-01619-8