Iwasawa theory for Galois extensions of number fields with restricted ramification and its applications

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Galois extensions of number fields with restricted ramification contain a lot of important information in number theory, for example the difficulty of unique prime factorization of higher dimensional integers. We studied the relationship between a related open problem in Iwasawa theory and non幼ommutative structure of the Galois extensions, and we gave new explicit examples. Moreover, we studied an analogous problem in knot theory in order to obtain new evidence of an unsolved conjecture.