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Title: Minimum Ramification for Finite Abelian Extensions Over Q and Q(i)
Keywords: minimum, ramification, abelian, extension, group, primes
Issue Date: 29-Dec-2010
Citation: OH SWEE LONG KEVIN (2010-12-29). Minimum Ramification for Finite Abelian Extensions Over Q and Q(i). ScholarBank@NUS Repository.
Abstract: The minimum number of finite primes that must ramify for a given finite abelian group to be realized over Q and Q(i) is given. To this end, we give a criterion for the existence of a surjection from a finitely generated abelian pro-pi group onto a finite abelian group. Class field theory is then applied to find the Galois group of the maximal abelian extension over Q and Q(i). The surjection criterion is then applied to each case to solve the minimum ramification of each finite abelian group.
Appears in Collections:Master's Theses (Open)

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