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Non-Abelian Groups and the Number of the Group Irreducible Character

Author: LiuZhiHui
Tutor: FanZuo
School: Wuhan University
Course: Basic mathematics
Keywords: Finite Groups Finite p-group Irreducible character Conjugated Commutator subgroup Centralizer
CLC: O152
Type: Master's thesis
Year: 2005
Downloads: 52
Quote: 0
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This paper studies the non-commutative finite group G is irreducible character counts and the link between the structure group G consists of the following two parts. The first part , note the order of a finite group G and the number of irreducible character ratio of μ (G), we studied the general non-commutative finite group G of the structure and μ (G) the relationship between the group G through order the smallest prime factor and commutator subgroup G ' was the smallest prime factor μ (G) is a lower bound , and gives a necessary and sufficient to achieve the lower bound condition . The second part , we have established a non-commutative finite p-group G with its conjugate relationship between the number of classes , and got smaller rank p-group G between the number of conjugacy classes with a more concise mutual determine relationships .

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