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1.
It is a well-known fact that characters of a finite group can give important information of the structure of the group. Also it was proved by the second author that a finite simple group can uniquely determined by its character table. Here the authors attempt to investigate how to characterize a finite group by using less information of its character table, and successfully characterize K 3-groups by their orders and one or two irreducible character degrees of their character tables. 相似文献
2.
It is a well-known fact that characters of a finite group can give
important information about the structure of the group. It was also
proved by the third author that a finite simple group can be
uniquely determined by its character table. Here the authors attempt
to investigate how to characterize a finite almost-simple group by
using less information of its character table, and successfully
characterize the automorphism groups of Mathieu groups by their
orders and at most two irreducible character degrees of their
character tables. 相似文献
3.
Recognizing the Automorphism Groups of Mathieu Groups Through Their Orders and Large Degrees of Their Irreducible Characters 下载免费PDF全文
《数学年刊B辑(英文版)》2016,(4)
It is a well-known fact that characters of a finite group can give important information about the structure of the group. It was also proved by the third author that a finite simple group can be uniquely determined by its character table. Here the authors attempt to investigate how to characterize a finite almost-simple group by using less information of its character table, and successfully characterize the automorphism groups of Mathieu groups by their orders and at most two irreducible character degrees of their character tables. 相似文献
4.
We compute the 13-modular character table of the bicyclic extension 2.Suz.2 given in the Atlas. This completes the last unknown modular character table of a bicyclic extension of the sporadic simple group Suz. We explain an issue of compatibility between different modular tables and partially recompute the 7-modular table of 2.Suz.2 in order to avoid such problems. 相似文献
5.
特征标表中零点个数很少的有限可解群 总被引:3,自引:1,他引:2
(1)与(2)均曾研究过有某特征标恰在两个共轭类上取非零值的有限群。本文讨论上述情形的另一极端,即每个不可约特征标至多在p个共轭类上取零值的有限可解群,这里p为群阶的最小素因子,通过对极小非交换商群的分析,我们将刻划这类群的结构。 相似文献
6.
Let G be a finite group, Irr(G) denotes the set of irreducible complex characters of G and gG the conjugacy class of G containing element g. A well-known theorem of Burnside([1,Theorem 3.15]) states that every nonlinear X ∈ Irr(G) has a zero on G, that is, an element x (or a conjugacy class xG) of G with X(x) = 0. So, if the number of zeros of character table is very small, we may expect, the structure of group is heavily restricted. For example, [2, Proposition 2.7] claimes that G is a Frobenius group with a complement of order 2 if each row in charcter table has at most one zero (its proof uses the classification of simple groups). In this note, we characterize the finite group G satisfying the following hypothesis: 相似文献
7.
In the ordinary character table of a finite group G, the values of the real valued irreducible characters on the real conjugacy classes form a sub-table which is square by Brauer's permutation lemma. We call this table the real part of the character table of G. Unlike the ordinary character table, viewed as a square matrix the real part of the character table is often singular. We present some results linking nonsingularity of this table to other properties of G. 相似文献
8.
Let U be a Sylow p-subgroup of the finite Chevalley group of type D4 over the field of q elements, where q is a power of a prime p. We describe a construction of the generic character table of U. 相似文献
9.
关于Camina条件 总被引:1,自引:0,他引:1
A.R.Camina曾研究过Frobenius群的一种类似.为此,他提出了两个假设并证明了这两个假设是等价的,在这篇文章中,我们提出比Camina假设弱且适合特征标表的两个假设,并证明我们的两个假设是等价的,然后,我们建立对这两个新假设而言最基本的情形的若干结果,这个最基本的情形被证明正好是有一个不可约特征标恰在两个共轭类上取非零值的群。 相似文献
10.
Patrick Headley 《Journal of Algebraic Combinatorics》1996,5(2):127-134
A combinatorial method of determining the characters of the alternating group is presented. We use matrix representations, due to Thrall, that are closely related to Young's orthogonal form of representations of the symmetric group. The characters are computed directly from matrix entries of these representations and entries of the character table of the symmetric group. 相似文献
11.
12.
Bounding the Fitting height of a solvable group by the number of zeros in a character table 总被引:1,自引:0,他引:1
Guohua Qian 《Proceedings of the American Mathematical Society》2002,130(11):3171-3176
In this paper, we bound the Fitting height of a solvable group by the number of zeros in a character table.
13.
Let cd(G) be the set of irreducible complex character degrees of a finite group G. The degree graph of G related to cd(G) was defined. It was proved many finite simple groups (but not all Mathieu groups) are uniquely determined by their orders and degree graphs. We hope to define a new graph related to cd(G) such that more simple groups can be uniquely determined by their orders and this newly defined graphs. Here a degree prime-power graph is defined and it is proved that all Mathieu groups can be determined uniquely by their orders and degree prime-power graphs. 相似文献
14.
Gabriel Navarro Benjamin Sambale Pham Huu Tiep 《Journal of Pure and Applied Algebra》2018,222(11):3721-3732
We give two ways to distinguish from the character table of a finite group G if a Sylow 2-subgroup of G has maximal class. We also characterize finite groups with Sylow 3-subgroups of order 3 in terms of their principal 3-block. 相似文献
15.
本文研究了有限(几乎)单群的非交换图刻画问题.利用有限几乎单群的阶分量理论,证明了对于具有非连通素图的有限单群,AAM猜想成立,同时也证明了某砦几乎单群也能被其非交换图刻画.上述结果推广了文献f131的结果.Abstract: In this article,we discuss the characterization of some finite(almost)simple groups by their non-commuting graphs.By using the theory of order components of finite almost simple groups,we prove that AAM's conjecture is true for all finite simple groups with non-connected prime graphs.Moreover,we prove that some almost simple groups can be also characterized by their non-commuting graphs.All the above results generalize those results in[13]. 相似文献
16.
By Brauer's induction theorem, for any finite group G, each irreducible complex character of G is a sum of characters induced from linear characters of elementary subgroups of G. The purpose of this note is to show that for soluble G, such a sum always exists in which the subgroups have their indices in G divisible by the degree of the character. 相似文献
17.
通过计算群中的对合数,本文刻画了以下两类有限群:特征标表中有一行至多有两个有理值的有限群;特征标表中有一列至多有两个实数值的有限群. 相似文献
18.
特征标次数的重数与可解群结构 总被引:2,自引:1,他引:1
非线性不可约特征标次数的重数全部为1的有限群的分类是熟知的.对可解群,本文讨论更一般的,即非线性不可约特征标次数的重数都与群阶互素的有限群的纯群论性质.特别地,得到了非线性不可约特征标次数的重数均小于2p的奇阶群G的分类结果.这里p为群阶|G|的最小素因子. 相似文献
19.
The spectrum of a finite group is the set of its element orders. We prove a theorem on the structure of a finite group whose spectrum is equal to the spectrum of a finite nonabelian simple group. The theorem can be applied to solving the problem of recognizability of finite simple groups by spectrum. 相似文献
20.
设G是有限群,H(?)G。如果H≌~2B_2(q)或H≌~2G_2(q)或H≌PSU(3,q),则G不与任何射影平面的点传递直射群同均。本文对以下问题给出了一般方法:证明以某些几乎单群为点传递自同构群的线性空间不是射影平面。 相似文献