廣西自然科學(xué)基金資助項(xiàng)目-資料下載頁
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【正文】 from to .According to the definition of automorphism. We know is an automorphism of . Notice that for any , we have and .In fact for any , it is clearly . Also , Thus .Since , say , we have known . We can obtain, .. Hence the proof of ≤is plete. It is easy to see that for every, if and only if where is the center of (short for ).Let be the mapping defined by , we will prove that is a group homomorphism from G onto I(G) and that C is its kernel.For every , we can readily find that , that is to say, is onto. For any , since , so that is a group homomorphism from onto .Notice that for any and every , we have , ., , that is . We obtain, hence . Next, for any , we know , . for any , , so that , say , thus . Therefore . Since is a group homomorphism of G onto and , according to the FHT, we have .Theorem 3 is a conclusion which the FHT apply group of inner automorphisms of a group. . Let me see an example that Theorem 3 applies it.Exercise 3. is a group, the center of is and ,then .References: １、近世代數(shù)初步，朱平天，李伯洪，鄒 園編，科學(xué)出版社，２００1年8月第一版２、近世代數(shù)基礎(chǔ)，劉邵學(xué)，高等教育出版社，１９９９年１０月第一版３、近世代數(shù)概論（上，下）王連祥，徐廣善譯，人民教育出版社，１９７９年１２月第一版環(huán)與代數(shù)，劉邵學(xué)著，科學(xué)出版社，１９８３年第一版近世代數(shù)引論， 馮克勤、李尚志、查建國(guó)、章璞編著，中國(guó)科技大學(xué)出版社2002年3月第二版群的基本同態(tài)定理的應(yīng)用李倩倩 劉志剛 楊立英（廣西師范學(xué)院 數(shù)學(xué)與計(jì)算機(jī)科學(xué)系， 南寧 530001） 摘要： 群的基本同態(tài)定理是群論研究中最常見、最有價(jià)值的結(jié)論之一。本文就該定理在群直積和內(nèi)同構(gòu)等方面的應(yīng)用進(jìn)行了討論并得到了一些有意義的結(jié)果。 關(guān)鍵詞：基本同態(tài)定理；直積；內(nèi)同構(gòu)。MR（2003）主題分類: 16W 中圖法分類: 文獻(xiàn)標(biāo)識(shí)法: A7 / 7
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