摘要本文研究有限群元素共轭类的平均长度问题。
This paper studies problem of the average length of conjugacy classes of finite groups.
有限群在某个极小子群共轭类上的某种传递性影响或决定群的构造。
The transitivity of a finite group on the conjugates of some minimal subgroups influences or determines the structure of the group.
辫群是一种非交换的无限群，该群中有许多困难问题是不可解的，如字问题、共轭问题和根问题等，利用这些困难问题可以去设计一些密码协议。
The braid group is infinite non-commutative group, and it has many hard problems that can be utilized to design cryptographic primitives, such as the word problem, conjugacy problem and root problem.
本文研究有限群元素共轭类的平均长度问题。
This paper studies problem of the average length of conjugacy classes of finite groups.
辫群是一种非交换的无限群，该群中有许多困难问题是不可解的，如字问题、共轭问题和根问题等，利用这些困难问题可以去设计一些密码协议。
The braid groups have many hard problems that can be utilized to design cryptographic primitives, for example, the word problem, conjugacy problem, and root problem.
第三章主要研究有限群的正规子群外的共轭类的个数对群结构的影响。
In Chapter 3, we investigate how the number of conjugacy classes outside a normal subgroup of a finite group influences its structure.
课题主要研究有限群的正规性条件及其对于有限群结构的确定和有限群的共轭类的长度对群结构的影响。
The project under research mainly focus on the different conditions of normality and the permutation of groups and use the normality to determine the structure of finite groups.
第二章主要研究有限群的中心外的同阶元的共轭类个数对群结构的影响。
In Chapter 2, we investigate how the number of conjugacy classes of elements outside the center with the same order of a finite group influences its structure.
文中，我们给出了有限极小非abel群的一个共轭类长——刻画并建立某些相关的结果。
In this paper, we give a conjugacy-class-length characterization of finite minimal non-abelian groups and establish some related results.
文中，我们给出了有限极小非abel群的一个共轭类长——刻画并建立某些相关的结果。
In this paper, we give a conjugacy-class-length characterization of finite minimal non-abelian groups and establish some related results.
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