[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki2\/archives\/3528#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki2\/archives\/3528","headline":"\u30d0\u30fc\u30f3\u30b5\u30a4\u30c9\u306e\u5b9a\u7406 – Wikipedia","name":"\u30d0\u30fc\u30f3\u30b5\u30a4\u30c9\u306e\u5b9a\u7406 – Wikipedia","description":"\u30a6\u30a3\u30ea\u30a2\u30e0\u30fb\u30d0\u30fc\u30f3\u30b5\u30a4\u30c9 \u6570\u5b66\u306b\u304a\u3051\u308b\u30d0\u30fc\u30f3\u30b5\u30a4\u30c9\u306e\u5b9a\u7406\uff08\u30d0\u30fc\u30f3\u30b5\u30a4\u30c9\u306e\u3066\u3044\u308a\u3001\u82f1: Burnside theorem\uff09\u306f\u3001\u4f4d\u6570\u304c\u7d20\u6570 p , q \u3068\u975e\u8ca0\u6574\u6570 a , b \u306b\u3088\u308a paqb\u00a0{displaystyle p^{a}q^{b} } \u3068\u66f8\u3051\u308b\u6709\u9650\u7fa4 G \u306f\u5fc5\u305a\u53ef\u89e3\u7fa4\u306b\u306a\u308b\u3053\u3068\u3092\u4e3b\u5f35\u3059\u308b\u7fa4\u8ad6\u306e\u5b9a\u7406\u3067\u3042\u308b\u3002\u3053\u308c\u3088\u308a\u3001\u4efb\u610f\u306e\u975e\u53ef\u63db\u306a\u6709\u9650\u5358\u7d14\u7fa4\u306e\u4f4d\u6570\u306f\u5c11\u306a\u304f\u3068\u30823\u500b\u4ee5\u4e0a\u306e\u7d20\u56e0\u6570\u3092\u6301\u305f\u306d\u3070\u306a\u3089\u306a\u3044\u3002 \u30d0\u30fc\u30f3\u30b5\u30a4\u30c9\u306e\u5b9a\u7406\u306f\u6b21\u306e\u30d5\u30a3\u30ea\u30c3\u30d7\u30fb\u30db\u30fc\u30eb\u306b\u3088\u308b\u540d\u9ad8\u3044\u53ef\u89e3\u7fa4\u306e\u7279\u5fb4\u3065\u3051\u306e\u7279\u5225\u306a\u5834\u5408\u3067\u3042\u308b\u3002 \u6709\u9650\u7fa4\u304c\u53ef\u89e3\u7fa4\u3067\u3042\u308b\u3053\u3068\u3068\u3001\u4efb\u610f\u306e\u7d20\u6570","datePublished":"2020-06-26","dateModified":"2020-06-26","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki2\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki2\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/8\/8c\/Burnside_2.jpeg\/220px-Burnside_2.jpeg","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/8\/8c\/Burnside_2.jpeg\/220px-Burnside_2.jpeg","height":"259","width":"220"},"url":"https:\/\/wiki.edu.vn\/jp\/wiki2\/archives\/3528","about":["Wiki"],"wordCount":3036,"articleBody":"  \u30a6\u30a3\u30ea\u30a2\u30e0\u30fb\u30d0\u30fc\u30f3\u30b5\u30a4\u30c9\u6570\u5b66\u306b\u304a\u3051\u308b\u30d0\u30fc\u30f3\u30b5\u30a4\u30c9\u306e\u5b9a\u7406\uff08\u30d0\u30fc\u30f3\u30b5\u30a4\u30c9\u306e\u3066\u3044\u308a\u3001\u82f1: Burnside theorem\uff09\u306f\u3001\u4f4d\u6570\u304c\u7d20\u6570 p , q \u3068\u975e\u8ca0\u6574\u6570 a , b \u306b\u3088\u308apaqb\u00a0{displaystyle p^{a}q^{b} }  \u3068\u66f8\u3051\u308b\u6709\u9650\u7fa4 G \u306f\u5fc5\u305a\u53ef\u89e3\u7fa4\u306b\u306a\u308b\u3053\u3068\u3092\u4e3b\u5f35\u3059\u308b\u7fa4\u8ad6\u306e\u5b9a\u7406\u3067\u3042\u308b\u3002\u3053\u308c\u3088\u308a\u3001\u4efb\u610f\u306e\u975e\u53ef\u63db\u306a\u6709\u9650\u5358\u7d14\u7fa4\u306e\u4f4d\u6570\u306f\u5c11\u306a\u304f\u3068\u30823\u500b\u4ee5\u4e0a\u306e\u7d20\u56e0\u6570\u3092\u6301\u305f\u306d\u3070\u306a\u3089\u306a\u3044\u3002  \u30d0\u30fc\u30f3\u30b5\u30a4\u30c9\u306e\u5b9a\u7406\u306f\u6b21\u306e\u30d5\u30a3\u30ea\u30c3\u30d7\u30fb\u30db\u30fc\u30eb\u306b\u3088\u308b\u540d\u9ad8\u3044\u53ef\u89e3\u7fa4\u306e\u7279\u5fb4\u3065\u3051\u306e\u7279\u5225\u306a\u5834\u5408\u3067\u3042\u308b\u3002\u6709\u9650\u7fa4\u304c\u53ef\u89e3\u7fa4\u3067\u3042\u308b\u3053\u3068\u3068\u3001\u4efb\u610f\u306e\u7d20\u6570 p \u306b\u95a2\u3057\u3066\u30db\u30fc\u30eb p\u2032-\u90e8\u5206\u7fa4\u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u306f\u540c\u5024\u3067\u3042\u308b[1]\u3002\u3053\u306e\u5b9a\u7406\u306f\u30a6\u30a3\u30ea\u30a2\u30e0\u30fb\u30d0\u30fc\u30f3\u30b5\u30a4\u30c9\u306b\u3088\u308a\u6709\u9650\u7fa4\u306e\u8868\u73fe\u8ad6\u3092\u4f7f\u3063\u3066\u8a3c\u660e\u3055\u308c\u305f(Burnside 1904)\u3002\u3044\u304f\u3064\u304b\u306e\u7279\u5225\u306a\u5834\u5408\u306f\u65e2\u306b\u30d0\u30fc\u30f3\u30b5\u30a4\u30c9\u3001\u30b8\u30e7\u30eb\u30c0\u30f3\u3001\u30d5\u30ed\u30d9\u30cb\u30a6\u30b9\u3068\u3044\u3063\u305f\u6570\u5b66\u8005\u306b\u3088\u3063\u3066\u8a3c\u660e\u304c\u4e0e\u3048\u3089\u308c\u3066\u3044\u305f\u3002\u30b8\u30e7\u30f3\u30fbG\u30fb\u30c8\u30f3\u30d7\u30bd\u30f3\u306f\u81ea\u8eab\u306eN\u7fa4\u306e\u7406\u8ad6\u306b\u3088\u3063\u3066\u8868\u73fe\u8ad6\u3092\u4f7f\u308f\u306a\u3044\u8a3c\u660e\u304c\u5f97\u3089\u308c\u308b\u3068\u6307\u6458\u3057\u3001\u5b9f\u969b\u306b\u4f4d\u6570\u304c\u5947\u6570\u306e\u5834\u5408\u306e\u8a3c\u660e(Goldschmidt 1970)\u3001\u4f4d\u6570\u304c\u5076\u6570\u306e\u5834\u5408\u306e\u8a3c\u660e(Bender 1972)\u304c\u4e0e\u3048\u3089\u308c\u305f\u3002Matsuyama (1973) \u306f\u8a3c\u660e\u3092\u7c21\u5358\u306b\u3057\u305f\u3002\u80cc\u7406\u6cd5\u306b\u3088\u308b\u3002p ,q \u3092\u56fa\u5b9a\u3059\u308b\u3002\u4f4d\u6570\u304c\u3053\u306e\u5f62\u3067\u66f8\u3051\u308b\u3088\u3046\u306a\u975e\u53ef\u89e3\u7fa4\u304c\u3082\u3057\u5b58\u5728\u3059\u308b\u306a\u3089\u3001\u305d\u306e\u4e2d\u3067\u4f4d\u6570\u304c\u6700\u5c0f\u3068\u306a\u308b\u3082\u306e\u304c\u3042\u308b\u304b\u3089\u3001\u306f\u3058\u3081\u304b\u3089 G \u304c\u305d\u306e\u3088\u3046\u306a\u4f4d\u6570\u6700\u5c0f\u306e\u7fa4\u3067\u3042\u308b\u3068\u3057\u3066\u3088\u3044\u3002  G \u306e\u4e2d\u5fc3 Z(G) \u306f\u5358\u4f4d\u5143\u306e\u307f\u304b\u3089\u306a\u308b\u3002\u307e\u305f a \u3082 b \u30820\u3067\u306a\u3044\u3002G \u304c\u81ea\u660e\u3067\u306a\u3044\u6b63\u898f\u90e8\u5206\u7fa4 H \u3092\u6301\u3066\u3070\u3001\u4f4d\u6570\u306e\u6700\u5c0f\u6027\u3088\u308a H \u3068\u5546\u7fa4 G\/H \u306f\u3068\u3082\u306b\u53ef\u89e3\u7fa4\u306b\u306a\u308b\u304b\u3089\u3001G \u3082\u53ef\u89e3\u7fa4\u3068\u306a\u3063\u3066\u77db\u76fe\u3059\u308b\u3002\u3088\u3063\u3066 G \u306f\u5358\u7d14\u7fa4\u3067\u3042\u308b\u3002G \u306e\u4e2d\u5fc3 Z(G) \u306f G \u306e\u6b63\u898f\u90e8\u5206\u7fa4\u3060\u304c\u3001G \u306f\u53ef\u63db\u7fa4\u3067\u306f\u3042\u308a\u5f97\u306a\u3044\u306e\u3067 G \u81ea\u8eab\u3068\u306f\u4e00\u81f4\u305b\u305a\u3001\u3088\u3063\u3066\u5358\u4f4d\u5143\u306e\u307f\u306b\u306a\u308b\u3057\u304b\u306a\u3044\u3002a \u307e\u305f\u306f b \u304c0\u3060\u3068\u3059\u308b\u3068\u3001G \u306f\u6709\u9650 q-\u7fa4\uff08\u307e\u305f\u306f\u6709\u9650 p-\u7fa4\uff09\u3067\u3042\u308a\u3001\u3088\u3063\u3066\u51aa\u96f6\u7fa4\u3068\u306a\u308a\u3001\u5f93\u3063\u3066\u53ef\u89e3\u7fa4\u306b\u306a\u3063\u3066\u77db\u76fe\u3059\u308b\u3002\u5171\u5f79\u985e\u306e\u5143\u306e\u500b\u6570\u304c qd \uff08 d > 0 \uff09\u3067\u3042\u308b\u3088\u3046\u306a G \u306e\u5143 g \u304c\u5b58\u5728\u3059\u308b\u3002\u30b7\u30ed\u30fc\u306e\u5b9a\u7406\u3088\u308a\u3001G \u306b\u306f\u4f4d\u6570 pa \u306e\u90e8\u5206\u7fa4 S \u304c\u5b58\u5728\u3059\u308b\u3002S \u306f\u975e\u81ea\u660e\u306a p-\u7fa4\u3060\u304b\u3089\u3001\u305d\u306e\u4e2d\u5fc3 Z(S) \u306f\u975e\u81ea\u660e\u3067\u3042\u308b\u3002\u305d\u3053\u3067\u5358\u4f4d\u5143\u3067\u306a\u3044 g\u2208Z(S){displaystyle gin Z(S)} \u304c\u3068\u308c\u308b\u3002g \u3068\u5171\u5f79\u306a\u5143\u306e\u500b\u6570\u306f\u5171\u5f79\u4f5c\u7528\u306b\u3064\u3044\u3066\u306e\u56fa\u5b9a\u90e8\u5206\u7fa4 Gg \u306e\u6307\u6570 [G\u00a0:\u00a0Gg] \u306b\u7b49\u3057\u304f\u3001\u305d\u308c\u306f S \u306e\u6307\u6570 qb \u3092\u5272\u308a\u5207\u308b\u3002\u306a\u305c\u306a\u3089 S \u306f Gg \u306e\u90e8\u5206\u7fa4\u3060\u304b\u3089\u3067\u3042\u308b\u3002\u3088\u3063\u3066\u5171\u5f79\u306a\u5143\u306e\u500b\u6570\u306f qd \u306e\u5f62\u306b\u66f8\u3051\u308b\u3002\u3055\u3089\u306b g \u306f\u5358\u4f4d\u5143\u3067\u306a\u304b\u3063\u305f\u304b\u3089 G \u306b\u304a\u3044\u3066\u4e2d\u5fc3\u7684\u3067\u306a\u304f\u3001\u6574\u6570 d \u306f\u6b63\u3067\u3042\u308b\u3002\u4ee5\u4e0b\u3001\u7fa4 G \u306e\u8907\u7d20\u6570\u4f53 C \u4e0a\u306e\u4e00\u822c\u7dda\u578b\u7fa4\u306b\u304a\u3051\u308b\u8868\u73fe\u3092\u8003\u5bdf\u3059\u308b\u3002G \u306e\u975e\u81ea\u660e\u306a\u65e2\u7d04\u8868\u73fe \u03c1\uff1aG \u2192 GLn(C) \u3068\u305d\u306e\u65e2\u7d04\u6307\u6a19 \u03c7 \u3067\u3001\u6b21\u5143 n \u304c q \u3067\u5272\u308a\u5207\u308c\u305a\u3001\u8907\u7d20\u6570 \u03c7(g) \u304c0\u306b\u306a\u3089\u306a\u3044\u3088\u3046\u306a\u3082\u306e\u304c\u5b58\u5728\u3059\u308b\u3002(\u03c7i)1\u2264i\u2264h \u3092 G \u306e C \u4e0a\u306e\u65e2\u7d04\u6307\u6a19\u5168\u4f53\uff08 \u03c71 \u306f\u81ea\u660e\u6307\u6a19\uff09\u3068\u3059\u308b\u3002g \u306f\u5358\u4f4d\u5143 1G \u3068\u5171\u5f79\u3067\u306a\u3044\u304b\u3089\u3001\u7fa4\u306e\u6307\u6a19\u8868\u306b\u304a\u3051\u308b\u76f4\u4ea4\u95a2\u4fc2\u3088\u308a0=\u2211i=1h\u03c7i(1G)\u03c7i(g)=1+\u2211i=2h\u03c7i(1G)\u03c7i(g){displaystyle 0=sum _{i=1}^{h}chi _{i}(1_{G})chi _{i}(g)=1+sum _{i=2}^{h}chi _{i}(1_{G})chi _{i}(g)}\u3053\u3053\u3067 \u03c7i(g) \u306f\u6b63\u5247\u884c\u5217 \u03c1(g) \u306e\u56fa\u6709\u5024\u306e\u548c\u306b\u7b49\u3057\u3044\u304c\u3001\u03c1(g) \u306e\u6700\u5c0f\u591a\u9805\u5f0f\u306f Tord\u2061(g)\u22121{displaystyle T^{operatorname {ord} (g)}-1} \u3092\u5272\u308a\u5207\u308b\u306e\u3067\u3001\u56fa\u6709\u5024\u306f\u307f\u306a1\u306e\u51aa\u6839\u3067\u3042\u308b\u3002\u3088\u3063\u3066 \u03c7i(g) \u306f\u4ee3\u6570\u7684\u6574\u6570\u3067\u3042\u308b\u3002\u3082\u3057\u3001\u03c7(g) \u304c0\u306b\u306a\u3089\u306a\u3044\u3088\u3046\u306a\u5168\u3066\u306e\u975e\u81ea\u660e\u306a\u65e2\u7d04\u6307\u6a19\u306b\u3064\u3044\u3066 \u03c7(1G) \u304c q \u3067\u5272\u308a\u5207\u308c\u308b\u306a\u3089\u3070\u22121q=\u2211i\u22652,\u00a0\u03c7i(g)\u22600\u03c7i(1G)q\u03c7i(g){displaystyle -{frac {1}{q}}=sum _{igeq 2,~chi _{i}(g)neq 0}{frac {chi _{i}(1_{G})}{q}}chi _{i}(g)}\u3068\u306a\u308b\u3002\u3068\u3053\u308d\u304c\u5de6\u8fba\u306f\u6709\u7406\u6574\u6570\u3067\u306a\u3044\u6709\u7406\u6570\u3060\u304b\u3089\u4ee3\u6570\u7684\u6574\u6570\u3067\u306f\u306a\u304f\u3001\u53f3\u8fba\u306f\u4ee3\u6570\u7684\u6574\u6570\u306e\u6709\u7406\u6574\u6570\u500d\u306e\u548c\u3060\u304b\u3089\u4ee3\u6570\u7684\u6574\u6570\u3067\u3042\u308a\u3001\u77db\u76fe\u3059\u308b\u3002\u3088\u3063\u3066\u671b\u3093\u3067\u3044\u305f\u6761\u4ef6\u3092\u6e80\u305f\u3059\u65e2\u7d04\u6307\u6a19\u306e\u5b58\u5728\u304c\u8a00\u3048\u305f\u3002\u8907\u7d20\u6570 qd\u03c7(g)\/n \u306f\u4ee3\u6570\u7684\u6574\u6570\u3067\u3042\u308b\u3002G \u4e0a\u306e\u4efb\u610f\u306e\u6709\u7406\u6574\u6570\u5024\u985e\u95a2\u6570 u \u306b\u5bfe\u3057\u3001\u7fa4\u74b0\u306e\u4e00\u822c\u8ad6\u3088\u308a1n\u2211s\u2208Gu(s)\u03c7i(s){displaystyle {frac {1}{n}}sum _{sin G}u_{(}s)chi _{i}(s)}\u306f\u6709\u7406\u6574\u6570\u74b0 Z \u4e0a\u6574\u3067\u3042\u308a\u3001\u7279\u306b g \u306e\u5171\u5f79\u985e\u4e0a\u30671\u3001\u305d\u308c\u4ee5\u5916\u30670\u3092\u3068\u308b\u3088\u3046\u306a\u985e\u95a2\u6570 u \u3092\u9078\u3093\u3060\u3068\u304d\u306e1n\u2211s\u2208Gu(s)\u03c7i(s)=qd\u03c7(g)n{displaystyle {frac {1}{n}}sum _{sin G}u_{(}s)chi _{i}(s)={frac {q^{d}chi (g)}{n}}}\u306f\u4ee3\u6570\u7684\u6574\u6570\u3067\u3042\u308b\u3002\u8907\u7d20\u6570 \u03c7(g)\/n \u306f\u4ee3\u6570\u7684\u6574\u6570\u3067\u3042\u308b\u3002q \u3068 n \u306f\u4e92\u3044\u306b\u7d20\u3060\u304b\u3089\u3001\u30d9\u30ba\u30fc\u306e\u88dc\u984c\u3088\u308a\u6709\u7406\u6574\u6570 x , y \u3067xqd+yn=1\u2234\u03c7(g)n=xqd\u03c7(g)n+y\u03c7(g){displaystyle xq^{d}+yn=1qquad therefore {frac {chi (g)}{n}}=x{frac {q^{d}chi (g)}{n}}+ychi (g)}\u3092\u6e80\u305f\u3059\u3082\u306e\u304c\u5b58\u5728\u3059\u308b\u3002\u3053\u306e\u5de6\u8fba\u306f\u4ee3\u6570\u7684\u6574\u6570\u306e\u6709\u7406\u6574\u6570\u500d\u306e\u548c\u3060\u304b\u3089\u3001\u4ee3\u6570\u7684\u6574\u6570\u306b\u306a\u308b\u3002g \u306e \u03c1 \u306b\u3088\u308b\u50cf\u306f\u5358\u4f4d\u884c\u5217\u306e\u8907\u7d20\u6570\u500d\u3067\u3042\u308b\u3002\u8907\u7d20\u6570 \u03b6\u00a0:= \u03c7(g)\/n \u306f\u4ee3\u6570\u7684\u6574\u6570\u3060\u304b\u3089\u3001\u305d\u306e\u30ce\u30eb\u30e0 N(\u03b6) \uff08 \u03b6 \u306e Q\u4e0a\u306e\u6700\u5c0f\u591a\u9805\u5f0f\u306e\u6839\u5168\u4f53\uff08\u5171\u5f79\u6570\uff09\u3092\u639b\u3051\u5408\u308f\u305b\u305f\u3082\u306e\uff09\u306f0\u3067\u306a\u3044\u6709\u7406\u6574\u6570\u306b\u306a\u308b\u3002\u03b6 \u304a\u3088\u3073\u305d\u306e\u5171\u5f79\u6570\u306f\u3044\u305a\u308c\u30821\u306e\u51aa\u6839\uff08\u03c1(g) \u306e\u56fa\u6709\u5024\uff09\u306e\u7b97\u8853\u5e73\u5747\u306a\u306e\u3067\u3001\u7d76\u5bfe\u5024\u306f1\u4ee5\u4e0b\u3067\u3042\u308b\u3002\u4e00\u65b9\u305d\u308c\u3089\u306e\u7a4d N(\u03b6) \u306f1\u4ee5\u4e0a\u3060\u304b\u3089\u3001\u7d76\u5bfe\u5024\u306f\u3061\u3087\u3046\u30691\u3067\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u3002\u7279\u306b \u03b6 \u306e\u7d76\u5bfe\u5024\u306f1\u3067\u3042\u308a\u3001\u3053\u308c\u306f \u03c1(g) \u306e\u56fa\u6709\u5024\u304c\u5168\u3066\u7b49\u3057\u3044\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u3002\u3088\u3063\u3066 \u03c1(g)  \u306e\u5bfe\u89d2\u5316\u3092\u8003\u3048\u308b\u3068\u3001 \u03c1(g) \u81ea\u8eab\u304c\u5358\u4f4d\u884c\u5217\u306e\u8907\u7d20\u6570\u500d\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002\u7d50\u8ad6N \u3092 \u03c1 \u306e\u6838\u3068\u3059\u308b\u3002\u03c1(g) \u306f\u50cf Im(\u03c1) \u306b\u304a\u3044\u3066\u4e2d\u5fc3\u7684\u3067\u3042\u308b\u304c\u3001 g \u306f G \u306b\u304a\u3044\u3066\u4e2d\u5fc3\u7684\u3067\u306f\u306a\u3044\u3002G\/N \u3068 Im(\u03c1) \u304c\u6a19\u6e96\u7684\u306b\u540c\u578b\u3067\u3042\u308b\uff08 xN\u21a6\u03c1(x){displaystyle xNmapsto rho (x)} \uff09\u3053\u3068\u3092\u8003\u3048\u308b\u3068\u3001N \u306f\u5358\u4f4d\u5143\u4ee5\u5916\u306e\u5143\u3092\u542b\u3080\u3002\u3053\u3053\u3067 G \u306f\u5358\u7d14\u7fa4\u3060\u304b\u3089\u3001N \u306f G \u3068\u4e00\u81f4\u3059\u308b\u3002\u3068\u3053\u308d\u304c\u3053\u308c\u306f\u3001 \u03c1 \u306f\u81ea\u660e\u8868\u73fe\u3067\u306a\u3044\u3068\u3057\u3066\u3044\u305f\u4eee\u5b9a\u3068\u77db\u76fe\u3059\u308b\u3002\u4ee5\u4e0a\u3088\u308a\u30d0\u30fc\u30f3\u30b5\u30a4\u30c9\u306e\u5b9a\u7406\u306f\u8a3c\u660e\u3055\u308c\u305f\u3002Q.E.D.\u53c2\u8003\u6587\u732e[\u7de8\u96c6]Bender, Helmut (1972), \u201cA group theoretic proof of Burnside’s paqb-theorem.\u201d, Math. Z. 126:  327\u2013338, doi:10.1007\/bf01110337, MR0322048\u00a0Burnside, W. (1904), \u201cOn Groups of Order p\u03b1q\u03b2\u201d, Proc. London Math. Soc. (s2-1 (1)):  388\u2013392, doi:10.1112\/plms\/s2-1.1.388\u00a0Goldschmidt, David M. (1970), \u201cA group theoretic proof of the paqb theorem for odd primes\u201d, Math. Z. 113:  373\u2013375, doi:10.1007\/bf01110506, MR0276338\u00a0James, Gordon; and Liebeck, Martin (2001). Representations and Characters of Groups (2nd ed.). Cambridge University Press. 0-521-00392-X.  See chapter 31.Matsuyama, Hiroshi (1973), \u201cSolvability of groups of order 2aqb.\u201d, Osaka J. Math. 10:  375\u2013378, MR0323890\u00a0"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki2\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki2\/archives\/3528#breadcrumbitem","name":"\u30d0\u30fc\u30f3\u30b5\u30a4\u30c9\u306e\u5b9a\u7406 – Wikipedia"}}]}]