On $p$-class groups of relative cyclic $p$-extensions

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 pseudo-null Iwasawa module over a certain 2-adic Lie extension.