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|Title||Some Congruences on Prime Factors of Class Number of Algebraic Extensions|
In this thesis, we study some congruences on the odd prime factors of the class number of the number fields. We say that a finite Galois extension L/K is Galois solvable if the Galois group Gal(L/K) is solvable. The main result studied is: Let L/Q be a finite algebraic extension with [L : Q] = 2α0 × N1, where N1 > 1 is odd. Suppose that there exists a field K ⊂ L with [K : Q] = 2α0 and with L/K Galois solvable extension. Let h(L) be the class number of L. Suppose that h(L) > 1. Let p be a prime dividing h(L). Let rp be the rank of the p-class group of L. If p × ∏ = (pi - 1) and N1 are coprime, then p divides the class number h(K) of K.
|Publisher||the islamic university|
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