# Journal of the Ramanujan Mathematical Society

Volume 39, Issue 3, September 2024 pp. 239–251.

Filtrations of Relative Units in the Cyclotomic ℤ{p}-extension of ℚ

**Authors**:
Takayuki Morisawa

**Author institution:**Division of Liberal Arts, Kogakuin University, 2665-1 Nakano, Hachioji, Tokyo, 192-0015, Japan.

**Summary: **
Let p be an odd prime number, n a non-negative integer and 𝔹{n} the n-th layer
of the cyclotomic ℤ{p}-extension of the rational number field. In this paper,
we focus our attention on the group of relative units of 𝔹{n}/𝔹{n−1}. We give two
different filtrations {𝒰{n}(j)}{j} and {ℰ{n}(k)}{k} of the group of relative units
and show that they have a relation.

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