{"id":61771,"date":"2024-04-09T09:29:35","date_gmt":"2024-04-09T09:29:35","guid":{"rendered":"https:\/\/science-hub.click\/%E5%90%8C%E5%9E%8B%E5%AE%9A%E7%90%86%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC\/"},"modified":"2024-04-09T09:29:35","modified_gmt":"2024-04-09T09:29:35","slug":"%E5%90%8C%E5%9E%8B%E5%AE%9A%E7%90%86%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=61771","title":{"rendered":"\u540c\u578b\u5b9a\u7406\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac"},"content":{"rendered":"<div><div><h2>\u5c0e\u5165<\/h2><p>\u6570\u5b66\u3067\u306f\u30013 \u3064\u306e<b>\u540c\u578b\u5b9a\u7406\u306b\u3088\u308a\u3001<\/b>\u7fa4\u7406\u8ad6\u306e\u67a0\u7d44\u307f\u5185\u3067\u306e\u540c\u578b\u306e\u5b58\u5728\u304c\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p><p>\u3053\u308c\u3089 3 \u3064\u306e\u540c\u578b\u5b9a\u7406\u306f\u3001\u7fa4\u4ee5\u5916\u306e\u69cb\u9020\u306b\u3082\u4e00\u822c\u5316\u3067\u304d\u307e\u3059\u3002\u7279\u306b<span><a href=\"https:\/\/science-hub.click\/?p=101783\">\u300c\u666e\u904d\u4ee3\u6570\u300d<\/a><\/span>\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u540c\u578b\u5b9a\u7406\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/qw6UTNhSrak\/0.jpg\" style=\"width:100%;\"\/><\/figure><h2>\u7b2c\u4e00\u540c\u578b\u5b9a\u7406<\/h2><p>\u6700\u521d\u306e\u540c\u578b\u5b9a\u7406\u306f\u3001\u7fa4\u306e\u5c04\u304c\u4e0e\u3048\u3089\u308c\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u8ff0\u3079\u3066\u3044\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {f:G\\to G&#8217;} $$<\/div> \u3001\u305d\u306e\u30ab\u30fc\u30cd\u30eb\u306b\u3088\u3063\u3066\u5546<span><i>G<\/i><\/span>\u306b\u3088\u3063\u3066<span><i>f \u3092<\/i><\/span>\u5358\u5c04\u7684\u306b\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p><p>\u76f4\u89b3\u7684\u306b\u306f\u3001\u30b0\u30eb\u30fc\u30d7<span><i>G \u3092<\/i><\/span>\u30b5\u30d6\u30b0\u30eb\u30fc\u30d7<span><i>H<\/i><\/span>\u3067\u5546\u3046\u3053\u3068\u306f\u3001 <span><i>H<\/i><\/span>\u306e\u8981\u7d20\u3092\u300c\u30ad\u30e3\u30f3\u30bb\u30eb\u300d\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001 <span><i>f<\/i><\/span>\u306e\u30ab\u30fc\u30cd\u30eb\u3067\u5546\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001 <span><i>f<\/i> ( <i>x<\/i> ) = 1<\/span>\u304c<span><i>x<\/i> = 1<\/span>\u306b\u5bfe\u3057\u3066\u306e\u307f\u771f\u3067\u3042\u308b\u3053\u3068\u304c\u4fdd\u8a3c\u3055\u308c\u3001\u3053\u308c\u306f<span><i>f<\/i><\/span>\u306e\u5358\u5c04\u6027\u3068\u540c\u7b49\u3067\u3059\u3002<\/p><p>\u7fa4\u5c04\u306b\u3064\u3044\u3066\u8a71\u305b\u308b\u3088\u3046\u306b\u306a\u308b<div class=\"math-formual notranslate\">$$ {G\/\\operatorname{Ker} f\\to G&#8217;} $$<\/div> \u3001\u307e\u305a\u5546\u304c\u30b0\u30eb\u30fc\u30d7\u69cb\u9020\u3067\u3042\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p><div><p><strong>\u547d\u984c<\/strong><span>\u2014<\/span> <span><i>G<\/i><\/span>\u3068<span><i>G<\/i> &#8216; \u3092<\/span>2 \u3064\u306e\u30b0\u30eb\u30fc\u30d7\u3068\u3057\u3001 <div class=\"math-formual notranslate\">$$ {f:G\\rightarrow G&#8217;} $$<\/div>\u7fa4\u306e\u5c04\u3002\u305d\u308c\u3067<div class=\"math-formual notranslate\">$$ {\\operatorname{Ker} f} $$<\/div>\u306f<span><i>G<\/i><\/span>\u306e\u6b63\u898f\u90e8\u5206\u7fa4\u3067\u3059\u3002<\/p><\/div><div><div><p>\u6ce8\u610f\u3057\u307e\u3057\u3087\u3046<div class=\"math-formual notranslate\">$$ {\\cdot} $$<\/div> <span><i>G<\/i><\/span>\u3068<span><i>G<\/i> &#8216;<\/span>\u306e\u6cd5\u5247\u3001\u304a\u3088\u3073<span><i>e<\/i><\/span>\u3068<span><i>e<\/i> &#8216;<\/span>\u306e\u4e2d\u7acb\u8981\u7d20\u3001\u305d\u3057\u3066\u6b21\u306e\u3053\u3068\u3092\u691c\u8a3c\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\operatorname{Ker} f} $$<\/div>\u5171\u5f79\u306b\u3088\u308a\u5b89\u5b9a\u3067\u3059\u3002\u3064\u307e\u308a\u3001 <div class=\"math-formual notranslate\">$$ {x\\cdot h\\cdot x^{-1}\\in\\operatorname{Ker} f} $$<\/div>\u3059\u3079\u3066\u306e\u305f\u3081\u306b<div class=\"math-formual notranslate\">$$ {x\\in G} $$<\/div>\u305d\u3057\u3066\u3059\u3079\u3066<div class=\"math-formual notranslate\">$$ {h\\in\\operatorname{Ker} f} $$<\/div> \u3002<\/p><p>\u6211\u3005\u306f\u6301\u3063\u3066\u3044\u307e\u3059<div class=\"math-formual notranslate\">$$ {f(x\\cdot h\\cdot x^{-1}) = f(x)\\cdot f(h)\\cdot f(x^{-1})} $$<\/div> \u3002 <span><i>h<\/i><\/span>\u304c\u5165\u3063\u3066\u3044\u308b\u306e\u3067<div class=\"math-formual notranslate\">$$ {\\operatorname{Ker} f} $$<\/div>\u3064\u307e\u308a\u3001 <span><i>f<\/i> ( <i>h<\/i> ) = <i>e<\/i> &#8216;<\/span>\u3067\u3042\u308b\u3068\u63a8\u6e2c\u3055\u308c\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {f(x\\cdot h\\cdot x^{-1}) = f(x)\\cdot f(x^{-1}) = f(x\\cdot x^{-1}) = f(e) = e&#8217;} $$<\/div> \u3002\u305d\u308c\u3067\u3001 <div class=\"math-formual notranslate\">$$ { x\\cdot h\\cdot x^{-1}} $$<\/div>\u3044\u308b<div class=\"math-formual notranslate\">$$ {\\operatorname{Ker} f} $$<\/div>\u305d\u3057\u3066<div class=\"math-formual notranslate\">$$ {\\operatorname{Ker} f} $$<\/div>\u3057\u305f\u304c\u3063\u3066\u3001 \u306f<span><i>G<\/i><\/span>\u306e\u6b63\u898f\u90e8\u5206\u7fa4\u3067\u3059\u3002<\/p><\/div><\/div><p>\u3068\u3044\u3046\u4e8b\u5b9f<div class=\"math-formual notranslate\">$$ {\\operatorname{Ker} f} $$<\/div> <span><i>G<\/i><\/span>\u306e\u6b63\u898f\u90e8\u5206\u7fa4\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u5546\u7fa4\u3067\u5b9a\u7fa9\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {G \/ \\operatorname{Ker} f} $$<\/div> <span><i>G<\/i><\/span>\u306e\u7fa4\u6cd5\u5247\u3068\u4e92\u63db\u6027\u306e\u3042\u308b\u7fa4\u6cd5\u5247\u3002\u3053\u306e\u4e92\u63db\u6027\u306e\u304a\u304b\u3052\u3067\u3001\u7fa4\u306e\u5c04\u306f<div class=\"math-formual notranslate\">$$ {f\u00a0: G \\rightarrow G&#8217;} $$<\/div>\u5c04\u3092\u8a98\u8d77\u3059\u308b<div class=\"math-formual notranslate\">$$ {\\widehat f\u00a0: G \/ \\operatorname{Ker} f \\rightarrow  \\operatorname{Im} f} $$<\/div> \u3002<\/p><p>\u3053\u308c\u3067\u5b9a\u7406\u3092\u8ff0\u3079\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p><div><p><strong>\u7b2c\u4e00\u540c\u578b\u5b9a\u7406<\/strong><span>\u2014<\/span> <span><i>G<\/i><\/span>\u3068<span><i>G<\/i> &#8216; \u3092<\/span>2 \u3064\u306e\u7fa4\u3068\u3057\u3001 <div class=\"math-formual notranslate\">$$ {f:G \\rightarrow G&#8217;} $$<\/div>\u7fa4\u306e\u5c04\u3002\u6b21\u306b\u3001 <span><i>f \u306f<\/i><\/span>\u6b21\u306e\u540c\u578b\u5199\u50cf\u3092\u5f15\u304d\u8d77\u3053\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {G\/\\operatorname{Ker} f} $$<\/div> <span><i>f<\/i> ( <i>G<\/i> )<\/span>\u306b\u5411\u304b\u3063\u3066\u3002<\/p><\/div><div><div><p> <span><i>H \u304c<\/i><\/span><span><i>f<\/i><\/span>\u306e\u30ab\u30fc\u30cd\u30eb\u3092\u8868\u3059\u3082\u306e\u3068\u3057\u307e\u3059\u3002\u79c1\u305f\u3061\u306f\u5b9a\u7fa9\u3057\u307e\u3059<div class=\"math-formual notranslate\">$$ {\\hat f} $$<\/div>\u30dd\u30fc\u30ba\u3092\u3068\u308b\u3053\u3068\u3067<\/p><dl><dd><div class=\"math-formual notranslate\">$$ {\\widehat f(xH) = f(x)} $$<\/div> \u3002<\/dd><\/dl><ul><li>\u6a5f\u80fd<div class=\"math-formual notranslate\">$$ {\\widehat f} $$<\/div>\u306f\u660e\u78ba\u306b\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3064\u307e\u308a\u3001 <div class=\"math-formual notranslate\">$$ {\\widehat f(xH)} $$<\/div>\u306f\u30af\u30e9\u30b9<span><i>x<\/i> <i>H<\/i><\/span>\u306b\u306e\u307f\u4f9d\u5b58\u3057\u3001\u7279\u5b9a\u306e\u4ee3\u8868<span><i>x<\/i><\/span>\u306b\u306f\u4f9d\u5b58\u3057\u307e\u305b\u3093\u3002<\/li><\/ul><p>\u78ba\u304b\u306b\u3001\u3082\u3057<div class=\"math-formual notranslate\">$$ {y\\in G} $$<\/div>\u306f<span><i>x<\/i> <i>H<\/i><\/span>\u306e\u3082\u3046 1 \u3064\u306e\u4ee3\u8868\u3067\u3059\u3002\u3064\u307e\u308a\u3001 <span><i>x<\/i> <i>H<\/i> = <i>y<\/i> <i>H<\/i><\/span>\u306e\u5834\u5408\u3001 <div class=\"math-formual notranslate\">$$ {xy^{-1}\\in H=\\operatorname{Ker} f} $$<\/div>\u3057\u305f\u304c\u3063\u3066\u3001 <span><i>f<\/i> ( <i>x<\/i> ) = <i>f<\/i> ( <i>y<\/i> )<\/span> \u3001\u3057\u305f\u304c\u3063\u3066<div class=\"math-formual notranslate\">$$ {\\widehat f(xH)=\\widehat f(yH)} $$<\/div> \u3002<\/p><ul><li>\u5546\u7fa4\u306e\u6cd5\u5247\u306e<span><a href=\"https:\/\/science-hub.click\/?p=74671\">\u5b9a\u7fa9<\/a><\/span>\u306b\u3088\u308a\u3001 <div class=\"math-formual notranslate\">$$ {\\widehat f} $$<\/div>\u306f\u7fa4\u306e\u5c04\u3067\u3059\u3002<\/li><\/ul><ul><li>\u5909\u5f62<div class=\"math-formual notranslate\">$$ {\\widehat f} $$<\/div>\u5168\u5c04\u7684\u3067\u3059:<\/li><\/ul><p>\u3059\u3079\u3066\u306e\u305f\u3081\u306b<div class=\"math-formual notranslate\">$$ {y\\in f(G)} $$<\/div> \u3001\u5b58\u5728\u3057\u307e\u3059<div class=\"math-formual notranslate\">$$ {x\\in G} $$<\/div> <span><i>f<\/i> ( <i>x<\/i> ) = <i>y<\/i><\/span>\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\u3057\u304b\u3057\u305d\u306e\u5f8c<div class=\"math-formual notranslate\">$$ {\\widehat f(xH)=f(x)=y} $$<\/div> \u3002<\/p><ul><li>\u5909\u5f62<div class=\"math-formual notranslate\">$$ {\\widehat f} $$<\/div>\u306f\u5358\u5c04\u3067\u3059\u3002<\/li><\/ul><p>\u5b9f\u969b\u3001 <span><i>x<\/i> <i>H \u3092<\/i><\/span>\u305d\u306e\u6838\u306e\u8981\u7d20\u3068\u3057\u307e\u3059\u3002\u305d\u308c\u3067<div class=\"math-formual notranslate\">$$ {e&#8217;=\\widehat f(xH)=f(x)} $$<\/div>\u3064\u307e\u308a\u3001 <span><i>x \u306f<\/i><\/span><span><i>f<\/i><\/span>\u306e\u30ab\u30fc\u30cd\u30eb<span><i>H<\/i><\/span>\u5185\u306b\u3042\u308a\u307e\u3059\u3002\u3057\u304b\u3057\u3001 <span><i>x<\/i> <i>H<\/i> = <i>H<\/i><\/span>\u3068\u306a\u308a\u3001\u3053\u308c\u306f<span><i>G<\/i> \/ <i>H<\/i><\/span>\u306e\u4e2d\u6027\u8981\u7d20\u306b\u306a\u308a\u307e\u3059\u3002<\/p><\/div><\/div><p>\u524d\u306e\u5b9a\u7406\u306e\u5225\u306e\u53ef\u80fd\u306a<span><a href=\"https:\/\/science-hub.click\/?p=97003\">\u5b9a\u5f0f\u5316\u306f<\/a><\/span>\u3001\u5c04<span><i>f \u304c<\/i><\/span>\u6b63\u6e96<span><a href=\"https:\/\/science-hub.click\/?p=32352\">\u5168\u5c04<\/a><\/span>\u3068<span><a href=\"https:\/\/science-hub.click\/?p=67765\">\u5c04\u51fa<\/a><\/span>\u306b\u3088\u3063\u3066\u56e0\u6570\u5206\u89e3\u3055\u308c\u308b\u3053\u3068\u3067\u3059\u3002\u3064\u307e\u308a\u3001\u6b21\u306e<span><a href=\"https:\/\/science-hub.click\/?p=47390\">\u56f3<\/a><\/span>\u306f\u53ef\u63db\u3067\u3059\u3002<\/p><div><div><div> <figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u6e96\u540c\u578b\u6027\u306e\u6b63\u6e96\u56e0\u6570\u5206\u89e3\u306e\u53ef\u63db\u56f3\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/vHIGTy1elno\/0.jpg\" style=\"width:100%;\"\/><\/figure><div>\u5c04\u306e\u56e0\u6570\u5206\u89e3<\/div><\/div><\/div><\/div><h2>\u7b2c 3 \u540c\u578b\u5b9a\u7406<\/h2><div><p><strong>\u7b2c\u4e09\u306e\u540c\u578b\u5b9a\u7406<\/strong><span>\u2014<\/span> <span><i>G \u3092<\/i><\/span>\u7fa4\u3001 <span><i>N<\/i><\/span>\u3068<span><i>M \u3092<\/i><\/span><span><i>G<\/i><\/span>\u306e 2 \u3064\u306e\u6b63\u898f\u90e8\u5206\u7fa4\u3068\u3059\u308b\u3002\u3053\u306e\u5834\u5408\u3001 <span><i>N<\/i> \/ <i>M \u306f<\/i><\/span><span><i>G<\/i> \/ <i>M<\/i><\/span>\u306e\u6b63\u898f\u90e8\u5206\u7fa4\u3068\u306a\u308a\u3001\u6b21\u306e\u540c\u578b\u6027\u304c\u5f97\u3089\u308c\u307e\u3059\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {(G\/M)\/(N\/M)\\simeq G\/N.} $$<\/div><\/dd><\/dl><\/div><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u540c\u578b\u5b9a\u7406\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/HFFi8hAiStE\/0.jpg\" style=\"width:100%;\"\/><\/figure><h2>\u7b2c\u4e8c\u540c\u578b\u5b9a\u7406<\/h2><div><p><strong>\u7b2c 2 \u540c\u578b\u5b9a\u7406<\/strong><span>\u2014<\/span> <span><i>G<\/i><\/span>\u3092\u7fa4\u3001 <span><i>N \u3092<\/i><\/span><span><i>G<\/i><\/span>\u306e\u6b63\u898f\u90e8\u5206\u7fa4\u3001 <span><i>H \u3092<\/i><\/span><span><i>G<\/i><\/span>\u306e\u90e8\u5206\u7fa4\u3068\u3059\u308b\u3002\u305d\u308c\u3067<div class=\"math-formual notranslate\">$$ {N \\cap H} $$<\/div>\u306f<span><i>H<\/i><\/span>\u306e\u6b63\u898f\u90e8\u5206\u7fa4\u3067\u3042\u308a\u3001\u6b21\u306e\u540c\u578b\u6027\u304c\u3042\u308a\u307e\u3059\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {H\/(H\\cap N)\\simeq HN\/N.} $$<\/div><\/dd><\/dl><\/div><div><div><ul><li>\u7fa4<span><i>H<\/i> <i>N<\/i> \/ <i>N<\/i><\/span>\u306b\u3064\u3044\u3066\u8a71\u305b\u308b\u3088\u3046\u306b\u3059\u308b\u306b\u306f\u3001\u307e\u305a<span><i>H<\/i> <i>N \u304c<\/i><\/span>\u7fa4\u3067\u3042\u308a\u3001 <span><i>N \u304c<\/i><\/span>\u6b63\u898f\u90e8\u5206\u7fa4\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3055\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\u3002<\/li><\/ul><p> <span><i>h<\/i> <i>n<\/i><\/span>\u3068<span><i>h<\/i> &#8216; <i>n<\/i> &#8216; \u3092<\/span><span><i>H<\/i> <i>N<\/i><\/span>\u306e 2 \u3064\u306e\u8981\u7d20\u3068\u3057\u307e\u3059\u3002 <span><i>h<\/i> <i>n<\/i> <i>h<\/i> &#8216; <i>n<\/i> &#8216; = <i>h<\/i> <i>h<\/i> &#8216;( <i>h<\/i> &#8216; <sup>\u2212 1<\/sup> <i>n<\/i> <i>h<\/i> &#8216;) <i>n<\/i> &#8216;<\/span>\u3068\u306a\u308a\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {hh&#8217;\\in H} $$<\/div> \u3001 <div class=\"math-formual notranslate\">$$ {h&#8217;^{-1}nh&#8217;\\in N} $$<\/div> ( <span><i>N \u306f<\/i><\/span><span><i>G<\/i><\/span>\u3067\u306f\u6b63\u898f\u306a\u306e\u3067) \u305d\u3057\u3066<div class=\"math-formual notranslate\">$$ {n&#8217;\\in N} $$<\/div>\u3057\u305f\u304c\u3063\u3066\u3001 <span><i>h<\/i> <i>n<\/i> <i>h<\/i> &#8216; <i>n<\/i> &#8216; \u306f<\/span><span><i>H<\/i> <i>N<\/i><\/span>\u5185\u306b\u3042\u308a\u3001\u3053\u308c\u306f<span><i>H<\/i> <i>N \u304c<\/i><\/span><span><a href=\"https:\/\/science-hub.click\/?p=57404\">\u4e57\u7b97<\/a><\/span>\u4e0b\u3067\u5b89\u5b9a\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/p><p>\u4e00\u65b9\u3067\u3001\u30b0\u30eb\u30fc\u30d7\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {N\\subset HN\\subset G} $$<\/div> \u3001 <span><i>N \u306f<\/i><\/span><span><i>G<\/i><\/span>\u3067\u6b63\u5e38\u3067\u3042\u308b\u305f\u3081\u3001 <span><i>HN<\/i><i>\u3067\u3082<\/i><\/span>\u6b63\u5e38\u3067\u3059\u3002<\/p><ul><li>\u540c\u578b\u6027\u3092\u78ba\u7acb\u3059\u308b\u305f\u3081\u306b\u3001\u6700\u521d\u306e\u540c\u578b\u6027\u5b9a\u7406\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002<\/li><\/ul><p>\u5c04\u5c04\u5c04\u304c\u3042\u308b<div class=\"math-formual notranslate\">$$ {j:H\\hookrightarrow HN} $$<\/div> <span><i>j<\/i> ( <i>h<\/i> ) = <i>h<\/i><\/span>\u304a\u3088\u3073\u6b63\u6e96\u5168\u5c04\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\sigma:HN\\twoheadrightarrow HN\/N} $$<\/div> ( <span><i>G<\/i><\/span>\u3067\u306f<span><i>N<\/i><\/span>\u304c\u6b63\u898f\u306a\u306e\u3067\u3001\u6700\u5f8c\u306e\u96c6\u5408\u306f\u30b0\u30eb\u30fc\u30d7\u3067\u3059)\u3002\u3053\u308c\u3089 2 \u3064\u306e\u5c04\u3092\u5408\u6210\u3059\u308b\u3068\u3001\u65b0\u3057\u3044\u5c04\u304c\u5f97\u3089\u308c\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {f=\\sigma\\circ j:H\\to HN\/N} $$<\/div> <span><i>f<\/i> ( <i>h<\/i> ) <i>=<\/i> <i>hN<\/i><\/span>\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002<\/p><ul><li>\u5c04<span><i>f \u306f<\/i><\/span>\u5168\u5c04\u3067\u3059\u3002<\/li><\/ul><p>\u78ba\u304b\u306b\u3001\u3069\u3061\u3089\u304b<div class=\"math-formual notranslate\">$$ {(hn)N\\in HN\/N} $$<\/div> \u3001 \u3068<div class=\"math-formual notranslate\">$$ {h\\in H} $$<\/div>\u305d\u3057\u3066<div class=\"math-formual notranslate\">$$ {n\\in N} $$<\/div> \u3002 <span><i>n \u306f<\/i><\/span><span><i>N<\/i><\/span>\u306b\u3042\u308b\u305f\u3081\u3001 <span><i>hnN<\/i> <i>=<\/i> <i>hN<\/i> <i>\u3001<\/i><i>\u3057\u305f\u304c\u3063\u3066<\/i><\/span><span><i>hnN<\/i> <i>=<\/i> <i>f<\/i> <i>(<\/i> <i>h<\/i> ) \u3068\u306a\u308a<\/span>\u307e\u3059\u3002<\/p><ul><li> <span><i>f<\/i><\/span>\u306e\u30ab\u30fc\u30cd\u30eb\u306f<div class=\"math-formual notranslate\">$$ {H\\cap N} $$<\/div> \u3002<\/li><\/ul><p>\u78ba\u304b\u306b\u3001 <span><i>f<\/i> ( <i>h<\/i> ) <i>=<\/i> <i>hN \u306f<\/i><\/span>\u3001 <span><i>h \u304c<\/i><\/span><span><i>N<\/i><\/span>\u306b\u3042\u308b\u5834\u5408\u306b\u9650\u308a\u3001 <span><i>HN<\/i> <i>\/<\/i> <i>N<\/i><\/span>\u306e\u4e2d\u6027\u8981\u7d20<span><i>N<\/i><\/span>\u3067\u3059\u3002 <span><i>h \u306f<\/i><\/span>\u3059\u3067\u306b<span><i>H<\/i><\/span>\u306b\u3042\u308b\u305f\u3081\u3001\u3053\u308c\u306f<span><i>h<\/i><\/span>\u304c H \u306b\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {N\\cap H} $$<\/div> \u3002<\/p><ul><li>\u6700\u521d\u306e\u540c\u578b\u5b9a\u7406\u306b\u3088\u308a\u3001\u6b21\u306e\u3053\u3068\u304c\u4fdd\u8a3c\u3055\u308c\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {N\\cap H} $$<\/div>\u306f<span><i>H<\/i><\/span>\u306e\u6b63\u898f\u90e8\u5206\u7fa4\u3067\u3042\u308a\u3001\u5c04\u306b\u3088\u3063\u3066\u6b21\u306e\u3053\u3068\u304c\u5c0e\u51fa\u3055\u308c\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\widehat f:H\/(N\\cap H)\\to HN\/N} $$<\/div>\u306f\u540c\u578b\u5199\u50cf\u3067\u3059\u3002<\/li><\/ul><\/div><\/div><\/div><h2 class=\"ref_link\">\u53c2\u8003\u8cc7\u6599<\/h2><ol><li><a class=\"notranslate\" href=\"https:\/\/ca.wikipedia.org\/wiki\/Teorema_d%27isomorfisme\">Teorema d&#8217;isomorfisme \u2013 catalan<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/cs.wikipedia.org\/wiki\/V%C4%9Bty_o_izomorfismu\">V\u011bty o izomorfismu \u2013 tch\u00e8que<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/de.wikipedia.org\/wiki\/Isomorphiesatz\">Isomorphiesatz \u2013 allemand<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/en.wikipedia.org\/wiki\/Isomorphism_theorems\">Isomorphism theorems \u2013 anglais<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/es.wikipedia.org\/wiki\/Teoremas_de_isomorfismo\">Teoremas de isomorfismo \u2013 espagnol<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/fa.wikipedia.org\/wiki\/%D9%82%D8%B6%D8%A7%DB%8C%D8%A7%DB%8C_%DB%8C%DA%A9%D8%B1%DB%8C%D8%AE%D8%AA%DB%8C\">\u0642\u0636\u0627\u06cc\u0627\u06cc \u06cc\u06a9\u0631\u06cc\u062e\u062a\u06cc \u2013 persan<\/a><\/li><\/ol><\/div>\n<div class=\"feature-video\">\n <h2>\n  \u540c\u578b\u5b9a\u7406\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n <div class=\"video-item\">\n  \n  <figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\">\n   <div class=\"wp-block-embed__wrapper\">\n    <iframe loading=\"lazy\" title=\"\u7b2c\u4e8c\u540c\u578b\u5b9a\u7406\uff3b\u5177\u4f53\u4f8b\u3067\u5b66\u3076\u4ee3\u6570\u5b66\u300a\u7fa4\u8ad6\u300bNo.19\uff3d\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/HyCqBO_Ja_c?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n   <\/div>\n  <\/figure>\n  \n <\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5c0e\u5165 \u6570\u5b66\u3067\u306f\u30013 \u3064\u306e\u540c\u578b\u5b9a\u7406\u306b\u3088\u308a\u3001\u7fa4\u7406\u8ad6\u306e\u67a0\u7d44\u307f\u5185\u3067\u306e\u540c\u578b\u306e\u5b58\u5728\u304c\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002 \u3053\u308c\u3089 3 \u3064\u306e\u540c\u578b\u5b9a\u7406\u306f\u3001\u7fa4\u4ee5\u5916\u306e\u69cb\u9020\u306b\u3082\u4e00\u822c\u5316\u3067\u304d\u307e\u3059\u3002\u7279\u306b\u300c\u666e\u904d\u4ee3\u6570\u300d\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002 \u7b2c\u4e00\u540c\u578b\u5b9a\u7406 \u6700\u521d\u306e\u540c\u578b\u5b9a\u7406\u306f\u3001 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":61772,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"https:\/\/img.youtube.com\/vi\/TNapSZBEZX4\/0.jpg","fifu_image_alt":"\u540c\u578b\u5b9a\u7406\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac","footnotes":""},"categories":[5],"tags":[58259,58258,11,13,10,14,12,1911,8,16,15,9],"class_list":["post-61771","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-dictionary","tag-cantalupo","tag-cantalupo-in-sabina","tag-techniques","tag-technologie","tag-actualite","tag-news","tag-dossier","tag-theoremes","tag-definition","tag-sciences","tag-article","tag-explications"],"_links":{"self":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts\/61771"}],"collection":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=61771"}],"version-history":[{"count":0,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts\/61771\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/media\/61772"}],"wp:attachment":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=61771"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=61771"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=61771"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}