[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/2966#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/2966","headline":"\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u90e8\u5206\u7fa4 – Wikipedia","name":"\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u90e8\u5206\u7fa4 – Wikipedia","description":"\u6570\u5b66\u3001\u7279\u306b\u7fa4\u8ad6\u3068\u547c\u3070\u308c\u308b\u4ee3\u6570\u5b66\u306e\u5206\u91ce\u306b\u304a\u3044\u3066\u3001\u6709\u9650\u7fa4 G \u306e\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u90e8\u5206\u7fa4\uff08\u82f1: Fitting subgroup\uff09 F(G) = Fit(G) \u3068\u306f\u3001G \u306e\u6700\u5927\u51aa\u96f6\u6b63\u898f\u90e8\u5206\u7fa4\u3067\u3042\u308b\u3002\u540d\u524d\u306f\u30cf\u30f3\u30b9\u30fb\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\uff08\u82f1\u8a9e\u7248\uff09\u306b\u7531\u6765\u3059\u308b\u3002\u76f4\u611f\u7684\u306b\u306f\u3001G \u304c\u53ef\u89e3\u7fa4\u306e\u3068\u304d\u3001\u7fa4 G \u5168\u4f53\u306e\u69cb\u9020\u3092\u3008\u7d71\u5236\u3009\u3059\u308b\u6700\u5c0f\u306e\u90e8\u5206\u7fa4\u306b\u76f8\u5f53\u3059\u308b\u3002\u7fa4 G \u304c\u53ef\u89e3\u3067\u306a\u3044\u3068\u304d\u3001\u4e00\u822c\u5316\u3055\u308c\u305f\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u90e8\u5206\u7fa4\uff08generalized Fitting subgroup\uff09 F*(G) = F(G)E(G)","datePublished":"2021-01-31","dateModified":"2021-01-31","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki\/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:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/982d99da779d667e6b17f09a357d7003cdee80e9","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/982d99da779d667e6b17f09a357d7003cdee80e9","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/2966","about":["Wiki"],"wordCount":2183,"articleBody":"\u6570\u5b66\u3001\u7279\u306b\u7fa4\u8ad6\u3068\u547c\u3070\u308c\u308b\u4ee3\u6570\u5b66\u306e\u5206\u91ce\u306b\u304a\u3044\u3066\u3001\u6709\u9650\u7fa4 G \u306e\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u90e8\u5206\u7fa4\uff08\u82f1: Fitting subgroup\uff09 F(G) = Fit(G) \u3068\u306f\u3001G \u306e\u6700\u5927\u51aa\u96f6\u6b63\u898f\u90e8\u5206\u7fa4\u3067\u3042\u308b\u3002\u540d\u524d\u306f\u30cf\u30f3\u30b9\u30fb\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\uff08\u82f1\u8a9e\u7248\uff09\u306b\u7531\u6765\u3059\u308b\u3002\u76f4\u611f\u7684\u306b\u306f\u3001G \u304c\u53ef\u89e3\u7fa4\u306e\u3068\u304d\u3001\u7fa4 G \u5168\u4f53\u306e\u69cb\u9020\u3092\u3008\u7d71\u5236\u3009\u3059\u308b\u6700\u5c0f\u306e\u90e8\u5206\u7fa4\u306b\u76f8\u5f53\u3059\u308b\u3002\u7fa4 G \u304c\u53ef\u89e3\u3067\u306a\u3044\u3068\u304d\u3001\u4e00\u822c\u5316\u3055\u308c\u305f\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u90e8\u5206\u7fa4\uff08generalized Fitting subgroup\uff09 F*(G) = F(G)E(G) \u304c\u540c\u69d8\u306e\u5f79\u5272\u3092\u679c\u305f\u3059\u3002\u3053\u3053\u3067 E(G) \u306f G \u306e\u6700\u5927\u534a\u5358\u7d14\u6b63\u898f\u90e8\u5206\u7fa4\u3067\u3042\u308b\u3002  \u6709\u9650\u3068\u306f\u9650\u3089\u306a\u3044\u4e00\u822c\u306e\u7fa4\u306b\u5bfe\u3057\u3066\u3001\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u90e8\u5206\u7fa4\u306f\u51aa\u96f6\u6b63\u898f\u90e8\u5206\u7fa4\u306b\u3088\u308a\u751f\u6210\u3055\u308c\u308b\u90e8\u5206\u7fa4\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u3002\u7121\u9650\u7fa4\u306e\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u90e8\u5206\u7fa4\u306f\u51aa\u96f6\u3067\u3042\u308b\u3068\u306f\u9650\u3089\u306a\u3044\u3002\u3053\u306e\u8a18\u4e8b\u3067\u306f\u5c02\u3089\u6709\u9650\u7fa4\u306e\u5834\u5408\u3092\u6271\u3046\u3002\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u90e8\u5206\u7fa4[\u7de8\u96c6]\u6709\u9650\u7fa4\u306e\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u90e8\u5206\u7fa4\u306e\u51aa\u96f6\u6027\u306f\u3001\u300c\u51aa\u96f6\u6b63\u898f\u90e8\u5206\u7fa4\u306e\u6709\u9650\u7a4d\u306f\u51aa\u96f6\u6b63\u898f\u90e8\u5206\u7fa4\u3067\u3042\u308b\u300d\u3068\u3044\u3046\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u306e\u5b9a\u7406\uff08\u82f1\u8a9e\u7248\uff09\u306b\u3088\u308a\u4fdd\u8a3c\u3055\u308c\u308b\u3002\u660e\u793a\u7684\u306b\u306f\u3001\u7fa4 G \u306e\u4f4d\u6570\u306b\u95a2\u3059\u308b\u7d20\u56e0\u6570 p \u306b\u6e21\u308b p-core Op(G) \u306e\u7a4d  F(G)=\u220fpOp(G){displaystyle F(G)=prod _{p}O_{p}(G)}\u3068\u3057\u3066\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u975e\u81ea\u660e\u306a\u6709\u9650\u53ef\u89e3\u7fa4 G \u306f\u975e\u81ea\u660e\u306a\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u90e8\u5206\u7fa4 F(G) \u3092\u6301\u3064\u3002\u3055\u3089\u306b\u51aa\u96f6\u3067\u306a\u3044\u6709\u9650\u7fa4 G \u306e\u5546 G\/F(G) \u306f\u975e\u81ea\u660e\u3067\u3042\u308b\u3053\u3068\u304b\u3089\u3001\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u5217\u306e\u9577\u3055\uff08\u82f1\u8a9e\u7248\uff09\u304c\u5b9a\u7fa9\u3055\u308c\u308b\u3002\u6709\u9650\u53ef\u89e3\u7fa4 G \u306e\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u90e8\u5206\u7fa4 F = F(G) \u306f\u81ea\u8eab\u306e\u4e2d\u5fc3\u5316\u7fa4\u3092\u542b\u3080\uff08\u3064\u307e\u308a  CG(F)\u2264F{displaystyle C_{G}(F)leq F}\u304c\u6210\u308a\u7acb\u3064\uff09\u306e\u3067\u3001\u3053\u308c\u306b\u3088\u308a\u6709\u9650\u53ef\u89e3\u7fa4 G \u306f\u51aa\u96f6\u7fa4 CG(F) = Z(F) \u306e\u51aa\u96f6\u7fa4\u306e\u5fe0\u5b9f\u306a\u81ea\u5df1\u540c\u578b\u7fa4 G\/Z(F) \u2264 Aut(F) \u306b\u3088\u308b\u62e1\u59271\u2192Z(F)\u2192G\u2192G\/Z(F)\u21921{displaystyle 1to Z(F)to Gto G\/Z(F)to 1}\u3068\u307f\u308b\u3053\u3068\u304c\u3067\u304d\u308b[1]\u3002\u51aa\u96f6\u7fa4\u306b\u304a\u3044\u3066\u3001\u4efb\u610f\u306e\u4e3b\u7d44\u6210\u56e0\u5b50\uff08\u82f1\u8a9e\u7248\uff09\u306f\u3059\u3079\u3066\u306e\u5143\u306b\u3088\u308a\u4e2d\u5fc3\u5316\u3055\u308c\u308b\u3002\u3053\u306e\u6761\u4ef6\u3092\u5e7e\u5206\u304b\u7de9\u3081\u3001\u4e00\u822c\u306e\u6709\u9650\u7fa4\u306b\u5bfe\u3057\u3066\u4efb\u610f\u306e\u4e3b\u7d44\u6210\u56e0\u5b50\u3092\u4e2d\u5fc3\u5316\u3059\u308b\u5143\u304b\u3089\u306a\u308b\u90e8\u5206\u7fa4\u3092\u3068\u308b\u3068\u3001\u518d\u3073\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u90e8\u5206\u7fa4\u3092\u5f97\u308b\uff1aF(G)=\u22c2{CG(H\/K):H\/K\u00a0is a cheif factor of\u00a0G}.{displaystyle F(G)=bigcap {,C_{G}(H\/K):H\/K{text{ is a cheif factor of }}G,}.}^ \u3057\u305f\u304c\u3063\u3066\u3001\u305f\u3068\u3048\u3070\u4f4d\u6570 |G| \u306f |Z(F)| |Aut(F)| \u306e\u7d04\u6570\u3067\u3042\u308b\u3002\u3053\u306e\u3053\u3068\u304b\u3089\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u90e8\u5206\u7fa4\u306e\u69cb\u9020\u306b\u3088\u308a\u53ef\u89e3\u7fa4\u5168\u4f53\u306e\u69cb\u9020\u306f\u304b\u306a\u308a\u306e\u7d71\u5236\u3092\u53d7\u3051\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002\u53c2\u8003\u6587\u732e[\u7de8\u96c6]Aschbacher, Michael (2000), Finite Group Theory, Cambridge University Press, ISBN\u00a0978-0-521-78675-1\u00a0Aschbacher, Michael; Seitz, Gary M. (1976), \u201cOn groups with a standard component of known type\u201d, Osaka J. Math. 13 (3):  439\u2013482\u00a0Bender, Helmut (1970), \u201cOn groups with abelian Sylow 2-subgroups\u201d, Mathematische Zeitschrift 117:  164\u2013176, doi:10.1007\/BF01109839, ISSN\u00a00025-5874, MR0288180\u00a0Huppert, B. (1967) (German), Endliche Gruppen, Berlin, New York: Springer-Verlag, ISBN\u00a0978-3-540-03825-2, MR0224703, OCLC\u00a0527050\u00a0Huppert, Bertram; Blackburn, Norman (1982), Finite groups. III., Grundlehren der Mathematischen Wissenschaften, 243, Berlin-New York: Springer-Verlag, ISBN\u00a03-540-10633-2, MR0650245\u00a0\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/2966#breadcrumbitem","name":"\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u90e8\u5206\u7fa4 – Wikipedia"}}]}]