【作者】 刘智慧；

【导师】 樊恽；

【作者基本信息】 武汉大学 ， 基础数学， 2005， 硕士

【摘要】 本文研究了非交换有限群G的不可约特征个数与群G结构之间的联系,由以下两个部分构成。 第一部分,记有限群G的阶与不可约特征标个数的比值为μ(G),我们研究了一般的非交换有限群G的结构和μ(G)之间的关系,通过群G的阶的最小素因子和换位子群G′的最小素因子得到了μ(G)的一个下界,同时给出了达到下界的一个充分必要条件。 第二部分,我们建立了非交换有限p-群G与其共轭类个数之间的关系,并且得到了较小阶的p-群G与其共轭类个数之间一种更简洁的相互决定关系。更多还原

【Abstract】 The thesis focus on the relationship between the number of irreducible character of a non-abelian finite group G and the structure of the group . It consists of the following two parts.The first part: Let μ(G) be the ratio of the order of a non-abelian finite group G to the number of irreducible character of the group. We establish a relation between μ(G) and the stucture of the group G, and obtain the lower bound of the ratio by the mininal prime divisor of the order and commutator of the group G, and give a necessary and sufficient condition under which this lower bound is attained.The second part: We study the connection between a non-abelian finite p-group G and the number of conjugacy class of it . We also find some more concise relationships between the minor order of a non-abelian finite p-group G and the number of conjugacy class of it .更多还原