{"author_name":"derwind","url":"https://randommemory.hatenablog.com/entry/2016/09/25/140321","height":"190","html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Frandommemory.hatenablog.com%2Fentry%2F2016%2F09%2F25%2F140321\" title=\"Galois\u7406\u8ad6(52)\u2015\u6709\u9650\u4f53\u306e\u5834\u5408\u306e\u30ac\u30ed\u30a2\u7fa4\u306e\u8a08\u7b97\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>","author_url":"https://blog.hatena.ne.jp/derwind/","blog_title":"\u3089\u3093\u3060\u3080\u306a\u8a18\u61b6","blog_url":"https://randommemory.hatenablog.com/","image_url":null,"title":"Galois\u7406\u8ad6(52)\u2015\u6709\u9650\u4f53\u306e\u5834\u5408\u306e\u30ac\u30ed\u30a2\u7fa4\u306e\u8a08\u7b97\u4f8b","published":"2016-09-25 14:03:21","width":"100%","type":"rich","categories":["math-alg"],"provider_name":"Hatena Blog","version":"1.0","provider_url":"https://hatena.blog","description":"\u98fd\u304d\u305f\u3089\u3084\u3081\u3088\u3046Galois\u7406\u8ad6(10)\u2015\u6709\u9650\u4f53 - \u3089\u3093\u3060\u3080\u306a\u8a18\u61b6\u3092\u601d\u3044\u51fa\u3059\u3068\u3001\u6709\u9650\u4f53\u306f\u305d\u306e\u7d20\u4f53 $K = \\mathbb{F}_p$ \u306b\u5bfe\u3057\u3066\u3001 $L = \\mathbb{F}_{p^n}$ \u3068\u540c\u578b\u3068\u306a\u308b\u306e\u3067\u3042\u3063\u305f\u3002 \u98fd\u304d\u305f\u3089\u3084\u3081\u3088\u3046Galois\u7406\u8ad6(21)\u2015\u5b8c\u5168\u4f53 - \u3089\u3093\u3060\u3080\u306a\u8a18\u61b6\u3068\u98fd\u304d\u305f\u3089\u3084\u3081\u3088\u3046Galois\u7406\u8ad6(11)\u2015\u6709\u9650\u4f53\u7d9a\u304d - \u3089\u3093\u3060\u3080\u306a\u8a18\u61b6\u3092\u601d\u3044\u51fa\u3059\u3068\u3001 $P \\in K[X]$ \u3092n\u6b21\u306e\u65e2\u7d04\u591a\u9805\u5f0f\u3068\u3059\u308b\u6642\u3001 $L$ \u306f $P$ \u306e\u5206\u89e3\u4f53\u3067\u3042\u308a\u3001\u304b\u3064\u5206\u96e2\u7684\u306a\u62e1\u5927\u4f53\u3067\u3042\u308b\u306e\u3067\u3001\u30ac\u30ed\u30a2\u62e1\u5927\u4f53\u3068\u306a\u308b\u3002 \u3067\u306f\u3001 $\\mathrm{Gal}(L/K) = \\mathrm{Gal}(\u2026"}