廣西自然科學(xué)基金資助項目-全文預(yù)覽
【正文】 pping 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、章璞編著，中國科技大學(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)與計算機科學(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、最有價值的結(jié)論之一。(3) for every and any .Definition 2. The kernel of a group homomorphism from to a group with identity is the set . The kernel of is denoted by .Definition 3. Let be a collection of groups. The external direct product of , 廣西自然科學(xué)基金(0447038)資助項目written as , is the set of all mtuples for which the its ponent is an element of , and the operation is ponentwise. In symbols =,where is defined to be Notice that it is easily to verify that the external dir
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