特征标群

Inspired by Burnside's theorem and the above other two propositions, we consider the question: whether the structure of a finite group G is restricted provided that the number of character zeros in its character table is"small"?

受Burnside定理及上述两命题的启发，我们考虑这样的问题：当G的特征标表中出现的零点个数"很少"时，是否G的群论结构有很大限制？

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

In the study of representations of finite group, lots of evidence suggested that there is a great relationship between the structure of conjugacy classes and the character degrees of finite group.

在群表示论的研究中，大量事实说明群的共轭类结构与群的特征标数量性质间存在着密切的关系。

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。

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。

Defined character degree's graph Г and proved that if Г is not connected then 2≤nl ≤4 for the Fitting height nl of solvable group G.

对有限群G，O.Manz等人定义了特征标次数图Γ，并且证明了：若Γ不连通，则可解群G的Fitiing高nl满足2≤nl≤4。

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。

In this paper, two conclusions are obtained, one is the connection between the subgroups of and the factor groups of finite abelian groups, and another is the character conditions of the subgroups with normal compelement.

文章主要包括两个结果，一个是关于有限交换群的子群与同态像之间的联系，另一个是关于子群有正规补的一个特征标刻划。

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。