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Class of finite groups isomorphic to keep some of the results from

Author: DuGuiQing
Tutor: HaiJinKe
School: Qingdao University
Course: Applied Mathematics
Keywords: Automorphism Class remain automorphism Central automorphisms Nilpotent class
CLC: O152.1
Type: Master's thesis
Year: 2010
Downloads: 18
Quote: 0
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Abstract


Class to maintain self- isomorphic finite group theory research is a hot topic of research in this paper, the results of previous studies on the basis of maintaining automorphism class made ??a further discussion, made ??the following aspects of work : This article in the second chapter gives the class to keep the automorphism group of the direct product decomposition in nature, and thus get a finite group G of class to keep the outer automorphism group is equal to 1 if and only if G is the direct product of each factor class to maintain outer automorphism group is equal to 1 ; in the third chapter , the establishment of classes to keep automorphism group is isomorphic with the center since the links between groups and self- help center isomorphic to some properties proved that if G is a a class 2 nilpotent finite p-group and its derivative subgroup is cyclic group , then G class to maintain outer automorphism group is equal to 1 , and also studied the center of G in G 's index of less than or equal p4 non- Abelian p-group G class to maintain outer automorphism group ; in Chapter abelian group is studied in this paper dihedral group expansion to keep this limited group of class outer automorphism group ; Finally, as a example, we verified the order of less than or equal p4 finite p-group G has a class to maintain outer automorphism group is equal to 1 .

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Group theory > Finite group theory
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