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《College Mathematics》 2018-01
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A Note on the Normal Subgroups

CHEN Yi-ping;School of Mathematics and Statistics,Wuhan University;  
The Cayley theorem plays an important role in modern algebras.Because it establishes a relation between a general abstract group Gand a symmetric group S_n.Namely,Gis isomorphic to a subgroup of S_n.So it is meaningful to study the subgroups of symmetric groups carefully.However,it is difficult for students to determine the normal subgroups precisely for the heavy computation.In this note,we give a method which occurs frequently in group theory and representation theory to decide the normal subgroups of symmetric groups.We hope that it will be useful for the beginners.
【Fund】: 国家自然科学基金(11301398);; 教育部新教师基金(20130141120035)
【CateGory Index】: O152.1
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