Some Conditions Implying Continuity of Maps

In this note, we study continuity of maps, in topological spaces, in terms of cluster points of images of convergent sequences and nets, and obtain some analogues of two results of Fuller [1].     

有限群的超可解性

本文利用子群格的模的性质对有限群进行研究 ,得到了有限超可解群的若干充分条件 ,推广了许多已有结果 .     

Character Values of Finite Groups

The aim of this paper is to describe simple methods to distribute the ordinary irreducible characters of finite groups into p-blocks and calculate the other character values from part of the values of the ordinary irreducible characters for p-blocks.2000 Mathematics Subject Classification: 20C20     

The Influence of Some Quantitative Properties of Abelian Subgroups on Solvability of Finite Groups

As an important application of Thompson's theorem [9 Robinson , D. J. S. ( 1996 ). A Course in the Theory of Groups. , 2nd ed. New York : Springer-Verlag .[Crossref] , [Google Scholar], Theorem 10.4.2], a finite group is solvable if it has an abelian maximal subgroup. In this article, we mainly investigate the influence of some quantitative properties of abelian subgroups on solvability of finite groups. Some new results are obtained.     

子群次正规性对有限群可解性的影响

考查了次正规子群对有限群结构的影响,得到有限群可解的若干充分条件和超可解的一个充分条件.     

有限群的某些定理

本文给出了有限群的如下结果：１）成为可解群与超可解群的条件；２）推广了Ｉｔｏ定理，３）超可解且内幂零的群结构。     

On the Solvability of Finite Irreducible Linear Groups with Hall TI-Subgroups

Conditions for a -solvable complex linear group of a relatively small degree to be solvable are found.     

Conditions Implying Self-adjointness of Operators

In this paper, we show that if is a quasi-class A operator and S is an arbitrary operator for which and ST = T*S, then T is self-adjoint, and we also show that quasisimilar quasi-class A operators have equal spectra and essential spectra. This work of the second author was supported by the University of Incheon Research Grant in 2008.     

On Some Groups with Finite Involution Saturated with Finite Simple Groups

In the paper, on the basis of the notion of saturation introduced in [1], we give a characterization of locally finite simple groups with an Abelian Sylow 2-subgroup in the classes of mixed and periodic groups. A part of the main results was announced in [2]. Theorem 2 of the paper generalizes results of [3, 4].     

Finite Groups with Nonmonomial Characters of Prime Degree

It is proved that every finite group for which the degrees of its nonmonomial characters are primes is solvable. The proof uses the classification of the finite simple groups.     

关于有限群特征标值的两点注记

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．     

Some Groups of Finite Homological Type

For each n≥ 0 we construct a torsion-free group that satisfies K.S. Brown’s FHT condition and is F _n (and hence FP _n ), but is not FP _n+1.I. J. Leary was partially supported by NSF grant DMS-0505471.M. Saadetoğlu was supported by the British Council and by the Ohio State Mathematical Research Institute     

Coleman Automorphisms of Extensions of Finite Characteristically Simple Groups by Some Finite Groups

Let G be an extension of a finite characteristically simple group by an abelian group or a finite simple group.It is shown that every Coleman automorphism of G is an inner automorphism.Interest in such automorphisms arises from the study of the normalizer problem for integral group rings.     

The Exterior Degree of a Pair of Finite Groups

The exterior degree of a pair of finite groups (G, N), which is a generalization of the exterior degree of finite groups, is the probability for two elements (g, n) in (G, N) such that g ? n = 1. In the present paper, we state some relations between this concept and the relative commutatively degree, capability and the Schur multiplier of a pair of groups.     

p-幂零群和p-闭群的若干充分条件

交换子群的中心化子和正规化子对有限群的结构有很强的控制作用,本文主要通过考虑某些交换子群的中心化子一致于正规化子,得到了p-幂零群和p-闭群的若干充分条件.     

p-幂零群的若干充分条件

群G的子群H称为半置换的,若对任意的K≤G,只要（｜H｜,｜K｜）=1．就有HK=KH,H称为s-半置换的,若对任意的p‖G｜,只要（p,｜H｜）=1,就有PH=HP,其中P∈Sylp（G）．本文利用Sylow子群的2-极大子群的s-半置换性得到有限群为p-幂零群的一些充分条件．