Page "Iwasawa theory" Paragraph 1

Iwasawa worked with so-called-extensions: infinite extensions of a number field with Galois group isomorphic to the additive group of p-adic integers for some prime p. Every closed subgroup of is of the form, so by Galois theory, a-extension is the same thing as a tower of fields such that.

Iwasawa studied classical Galois modules over by asking questions about the structure of modules over.