Korean J. Math. Vol. 30 No. 2 (2022) pp.361-362
DOI: https://doi.org/10.11568/kjm.2022.30.2.361

On the lower layers of a $\mathbb Z_{p}$-extension

Main Article Content

Jangheon Oh


It is shown that the $p$-part of the class number of the lower layers of a cyclotomic $\mathbb Z_{p}$-extension can grow exponentially.

Article Details


[1] K.Iwasawa, On Zl-extensions of algebraic number fields, Ann.of Math. 98 (2) (1973), 246–326. Google Scholar

[2] T.Kataoka, A consequence of Greenberg’s generalized conjecture on Iwasawa invariants of Zp- extensions, Journal of Number Theory 172 (3) (2017), 200–233. Google Scholar

[3] J.Minardi, Iwasawa modules for Zdp-extensions of algebraic number fields, Ph.D dissertation, University of Washington, 1986. Google Scholar

[4] L.Washington, Introduction to Cyclotomic Fields, Grad. Texts in Math., 83, Springer-Verlag, New York(1982). Google Scholar