不可约特征标

For a finite group G, an old theorem of Burnside asserts: each non-linear irreducible character of G must vanish on some element.

设G为有限群，古老的Burnside定理指出：G的每个非线性不可约特征标至少在一个共轭类上取零值。

For a character χ of finite group G, set

设χ为有限群G的一个不可约特征标，令

We establish a relation between μ 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.

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，我们研究了一般的非交换有限群G的结构和μ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的一个下界，同时给出了达到下界的一个充分必要条件。

Given a p-solvable group G and an irreducible Brauer character χof G with respect to the prime p.

给定一个p-可解群G以及G的一个关于该素数p的不可约B rauer特征标χ。

Irreducible character; zero point of character; character table

不可约特征标；特征标零点；特征标表

For a Hall π-subgroup in π-separable group and a given π-Fong character, we show that there always exists a normal subgroup, such that some irreducible constituent of this π-Fong character which restricts on the join of these two subgroups is a π-Fong character associated to this normal subgroup.

对于π-可分群的一个Hall π-子群和一个给定的π-Fong特征标，我们证明了总存在一个正规子群使得这个π-Fong特征标在这两个子群的交上的限制的某个不可约成分是联系这个正规子群的一个π-Fong特征标。

In section four, we consider a normal π-subgroup in π-separable group, a normal set and a complex value class function space defined on G, using the B_π-character theory and character-triple isomorphism, and find a classical basis of this space such that it behaves as the set of irreducible Brauer characters, and satisfies the Fong-Swan property.

在第四节中我们考虑了π-可分群G中的一个正规π-子群，以及定义在G上的一个正规集和它上面的一个复值类函数空间，利用B_π-特征标理论和特征三元组同构，我们找到了这个空间的一个经典基，使得这个基具有类似于不可约Brauer特征标的集合的性质，并且满足Fong-Swan性质。

Faithful irreducible characters play an important role in the studying of products of characters.

忠实不可约特征标在特征标乘积的研究中起着很重要的作用。

Chapter 12 deals with the commectios between the set of degrees of the irreducible characters and the structure of a group.

第12章主要研究不可约特征标次数集合和群结构之间的关系。第13章主要是对Glauberman的一篇论文的解释。

We first characterize the groups in which all m∈cdq〓 contain at most 4 prime divisors; and then show the following: if any m∈cdq〓 is nth-power-free then the derived length of solvable group G is bounded by a function f depended only on n; also if cdq〓 has k different p-parts then the p-length of solvable group G is bounded by a function g depended only on k.

首先研究了非线性不可约特征标对应的特征标次数的商至多含有4个素因子的有限群结构。其次，我们证明：若每m∈cdq〓是n次方自由的，则有限可解群G的的导长及p-长都被仅依赖于n的函数所界定；若cdq〓中共有k个两两不同的p-部分，则有限可解群G的p-长能被仅依赖于k的函数所界定。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。