Ấn phẩm:
On the Galois groups of the 2-class field towers of some imaginary quadratic fields
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Let k be a number field, p a prime, and knr p the maximal unrami ed p-extension of k. Golod and Shafarevich focused the study of knr ,p/k on Gal(knr 'p/k). Let S be a set of primes of k (in nite or finite), and kS the maximal p-extension of k unrami ed outside S. Nigel Boston and C.R. Leedham-Green introduced a method that computes a presentation for Gal(kS k) in certain cases. Taking S = {(1) , Michael Bush used this method to compute possibilities for Gal(knr 2 k) for the imaginary quadratic fields k = Q( -2379) , Q( -445) , Q( -1015), and Q( -1595). In the case that k = Q( -2379), we illustrate a method that reduces the number of Bush's possibilities for Gal(knr ,2/k) from 8 to 4. In the last 3 cases, we are not able to use the method to isolate Gal(knr ,2/k)However, the results in the attempt reveal parallels between the possibilities for Gal(knr 2 k) for each field. These patterns give rise to a class of group extensions that includes each of the 3 groups. We conjecture subgroup and quotient group properties of these extensions.
Tác giả
Steurer, Aliza
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Nơi xuất bản
Nhà xuất bản
University of Maryland
Năm xuất bản
2006
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Từ khóa chủ đề
Tón học , Galois groups