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|Title:||Minimum Ramification for Finite Abelian Extensions Over Q and Q(i)||Authors:||OH SWEE LONG KEVIN||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.||URI:||http://scholarbank.nus.edu.sg/handle/10635/23764|
|Appears in Collections:||Master's Theses (Open)|
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