p-TOWER GROUPS OVER QUADRATIC IMAGINARY NUMBER FIELDS
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چکیده
The modern theory of class field towers has its origins in the study of the p-class field tower over a quadratic imaginary number field, so it is fitting that this problem be the first in the discipline to be nearing a solution. We survey the state of the subject and present a new cohomological condition for a quadratic imaginary number field to have an infinite p-class field tower (for p odd). Under an additional hypothesis, we refine this to a necessary and sufficient condition and describe an algorithm for evaluating this condition for a given quadratic imaginary number field.
منابع مشابه
Imaginary Quadratic
is called the 2-class field tower of k. If n is the minimal integer such that kn = kn+1, then n is called the length of the tower. If no such n exists, then the tower is said to be of infinite length. At present there is no known decision procedure to determine whether or not the (2-)class field tower of a given field k is infinite. However, it is known by group theoretic results (see [2]) that...
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