Structure of l-class groups of certain number fields and ℤ<sub>l</sub>-extensions
Gerth, Frank; Gerth Frank; The Universtity of Texas
Журнал:
Mathematika
Дата:
1977
Аннотация:
Let l be a rational prime, and let ℤ<sub>l</sub> denote the ring of l-adic integers. Let k<sub>0</sub> be a finite extension field of the rational numbers ℚ, and let K be a ℤ<sub>l</sub>-extension of k<sub>0</sub> (i.e., Gal (K/k<sub>0</sub>) is topologically isomorphic to the additive group of Z<sub>l</sub>). Let the intermediate fields be denoted as follows:where k<sub>n</sub>k<sub>0</sub> is a cyclic extension of degree l<sub>n</sub>, and Let A<sub>n</sub> denote the l-class group of k<sub>n</sub> (i.e., the Sylow l-subgroup of the ideal class group of k<sub>n</sub>). It is known that the order of A<sub>n</sub> is given by , with
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