{"published":"2016-10-08 23:22:54","height":"190","provider_name":"Hatena Blog","html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Frandommemory.hatenablog.com%2Fentry%2F2016%2F10%2F08%2F232254\" title=\"Galois\u7406\u8ad6(58)\u2015\u5186\u5206\u62e1\u5927\u306e\u4f8b - \u3089\u3093\u3060\u3080\u306a\u8a18\u61b6\" class=\"embed-card embed-blogcard\" scrolling=\"no\" frameborder=\"0\" style=\"display: block; width: 100%; height: 190px; max-width: 500px; margin: 10px 0px;\"></iframe>","provider_url":"https://hatena.blog","width":"100%","url":"https://randommemory.hatenablog.com/entry/2016/10/08/232254","type":"rich","blog_title":"\u3089\u3093\u3060\u3080\u306a\u8a18\u61b6","version":"1.0","author_url":"https://blog.hatena.ne.jp/derwind/","blog_url":"https://randommemory.hatenablog.com/","title":"Galois\u7406\u8ad6(58)\u2015\u5186\u5206\u62e1\u5927\u306e\u4f8b","categories":["math-alg"],"author_name":"derwind","description":"$\\zeta_n := \\exp(2\\pi i/n)$ \u3068\u7f6e\u304f\u3002 $L = \\Q(\\zeta_n)$ \u3068\u3059\u308b\u3068\u3001 $L/\\Q$ \u306f\u30ac\u30ed\u30a2\u62e1\u5927\u3067\u3042\u308a\u3001 $\\mathrm{Gal}(L/\\Q) \\simeq (\\Z/n\\Z)^\\times$ \u3067\u3042\u3063\u305f\u3002(Galois\u7406\u8ad6(57)\u2015\u5186\u5206\u591a\u9805\u5f0f\u306e\u65e2\u7d04\u6027\u3068\u5186\u5206\u62e1\u5927 - \u3089\u3093\u3060\u3080\u306a\u8a18\u61b6) \u4f8b $n = 8$ \u306e\u5834\u5408\u3002 $(\\Z/8\\Z)^\\times = \\{1,3,5,7\\}$ \u3067\u3042\u308a\u3001 $\\#( (\\Z/8\\Z)^\\times) = 4$ \u3067\u3042\u308b\u3002\u3053\u308c\u306b\u5bfe\u5fdc\u3059\u308b\u30ac\u30ed\u30a2\u7fa4\u3092 $\\mathrm{Gal}(L/\\Q) =\\{id, \\sigma_3, \\si\u2026","image_url":null}