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We study the structure of the Galois group of the maximal unramified 2-extension of some family of number fields of large degree. Especially, we show that for each positive integer  n , there exist infinitely many number fields with large degree, for which the defined Galois group is quaternion of order 2  n  .

On the 2-class field tower of subfields of some cyclotomic ℤ 2 -extensions