@article{oai:teapot.lib.ocha.ac.jp:00034857,
 author = {Onabe, Midori},
 issue = {2},
 journal = {お茶の水女子大學自然科學報告},
 month = {Dec},
 note = {application/pdf, 紀要論文, Let Q be the rational number field. For any algebraic number field k of finite degree over Q, we shall denote by A_k the maximal abelian extension of k and by Gal(A_k/k) the Galois group of A_k over k equipped with the Krull topology. The present paper exhibits some counterexamples to the following statement ; for two algebraic number fields k and k' of finite degree over Q, an isomorphism Gal(A_k/k)≅Gal(A_k'/k') of the Galois groups of maximal abelian extensions A_k/k and A_k'/k' implies an isomorphism k≅k'. In other words we shall see that Gal(A_k/k) does not determine the isomorphism class of an algebraic number field k. Furthermore, the counterexamples which we give will show that even if Gal(A_k/k) and Gal(A_k'/k') are isomorphic, the ideal class groups of k and k' are not necessarily isomorphic.},
 pages = {155--161},
 title = {On the Isomorphisms of the Galois Groups of the Maximal Abelian Extensions of Imaginary Quadratic Fields},
 volume = {27},
 year = {1976}
}