Alguns resultados sobre o grupo das classes dos corpos quadráticos

• Ano de defesa: 2017
• Autor(a) principal: Sousa, Flaviano Frota
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Palavras-chave em Português: Discrimantes; Corpos quadráticos reais e imaginários; Grupo das classes
• Link de acesso: http://www.repositorio.ufc.br/handle/riufc/24766

Many are the known results involving the groups of numbers elds and many are the open problems. We know that the group of classes of a number fields is finite and abelian. In this paper we present some results about the group of the classes of the quadratic fields. It is known that for every intergers n greater than zero there are finite quadratic fields, both real and imaginary, whose class groups have a cyclic subgroup of order n. For an arbitrary abelian group G of order n, the existence or not of finite quadratic fields with groups of ideal classes having a subgroup isomorphic to G is an open problem. Particularly for non-cyclic finite abelian groups G, Kwang-Seob Kim has proved that there are finite real quadratic bodies in G =Z/nZ x Z/nZ: Whose groups of ideal classes contains a subgroup isomorphic to G and that is G = Z/nZ x Z/nZxZ/nZ then there are finite imaginary quadratic cups whose groups of ideal classes contain a subgroup isomorphic to G. The theorem of Kwang-Seob Kim is the main result presented in this dissertation.