两个有限超可解群的积

讨论了有限群G是两个有限群A,B之积时的超可解性的问题.利用半正规和拟正规的概念,在较弱的条件下给出了群G超可解的一些充分条件.

Abstract：

The supersoluability of a finite group G when it is the product G of two finite supersoluable groups A and B is discussed. Some sufficient conditions of the supersoluability of G are obtained under some weaker hypotheses by using the concept of semi-normality and quasi-normality which generalize the known.     

恰含两个非线性Monolith特征标的有限群

对恰含两个非线性monolith特征标的有限群作分类研究,证明这种群共分9类,并给出了它们的群论结构.

Abstract：

The monolithic characters influence mostly the structure of a finite group by the studies of I. Isaacs, Y. Berkovich and others. In this article we prove that the groups which have exactly two nonlinear monolith characters are classified into nine classes, and their group structures are described.     

关于极大子群的θ*-偶

主要利用θ*-偶来研究群G的结构,得到了有限群可解和超可解的一些新的描述.     

再论能表示为三个真子群的并的群

给出了一个群能表示为三个真子群的并的一个简单证明;证明了一个群只有三个极大子群且能表示为三个真子群的并当且仅当这个群是二元生成2群.

Abstract：

It was discussed many years ago that a group could be the union of three distinct proper subgroups. Recently, the proof has been simplified, but remains complicated. A very simple proof is given for this result in this article, and the finite group that can be written into the union of three distinct proper subgroups and has exactly three maxinmal subgroups is classified.     

有限群的完全c-置换子群与超可解性

利用完全c-置换子群的概念,得到了有限群超可解的两个充分条件:(1)如果群G的4阶循环子群在G中完全c-置换且G的任意极小子群含于G的超可解超中心Zμ(G)中,那么G是超可解群;(2)设NG且G/N是超可解群。如果N的任意4阶循环子群在G中完全c-置换且N的任意极小子群包含在G的超可解超中心Zμ(G)中,那么G是超可解群。     

弱拟正规子群对有限群结构的影响

对任意有限群G，利用其子群的弱拟正规条件刻划原群G的结构，给出G超可解的若干充分条件。     

最高阶元个数为10p^m的有限群是可解群

讨论了最高阶元素个数｜M（G）｜=10p^m的有限群,其中p为不小于5的素数,m为自然数.证明了这类群是可解群.     

最高阶元个数为10pm的有限群是可解群

讨论了最高阶元素个数|M(G)|=10pm的有限群,其中p为不小于5的素数,m为自然数.证明了这类群是可解群.     

恰有7个非正规子群的有限群

利用非正规子群的共轭类类数为1,2的有限群的结构,给出了恰有7个非正规子群的有限群的完全分类.定理1 若有限群G恰有7个非正规子群,则G同构于以下群之一.(1)〈x,y|x~7=y~(2~n)=1,x~y=x~(-1),n≥1〉.(2)〈x,y | x~7=Y~(3~n)=1,x~y=x~4≥1〉.(3)A_4.(4)〈x,y| x~7=y~(7~n)=1,x~y=x~(1+7~(n-1)),n≥2〉.

Abstract：

Using the results of non-normal subgroups with 1 and 2 conjugate classes,a complete classification of finite groups with seven non-normal subgroups is given.     

关于区间直觉模糊多属性群决策中专家意见一致度的集结

本文首先给出了区间直觉模糊距离的定义,并在此基础上,提出了一种集结区间直觉模糊多属性群决策中专家个人意见的一致度的新方法.最后,给以实例用来说明此方法的具体应用.

Abstract：

The concept of interval-valued intuitionistic fuzzy distance is defined. Based on this definition, a new method for solving the problem of consensus degree aggregation of experts' opinions in the multi-attribute group decision-making is proposed. Finally, a numerical example is given to show how to apply this method.     

有限群可解的若干充分条件

称群G的一个子群H在G中弱拟c-正规,如果存在G的一个次正规子群K,使得H∩K为G的次正规子群,KH成群并且满足|G∶KH|为素数幂.利用子群的弱拟c-正规性给出了一个群为可解群的若干充分条件.     

某些子群的覆盖-远离性质对有限群结构的影响

利用覆盖-远离子群的概念研究了群的超可解性和幂零性. 首先利用有限群G的Fitting子群和Sylow子群的覆盖-远离性质给出了关于G超可解的几个充分条件; 然后再对G的Sylow子群的正规化子等的覆盖-远离性质进行讨论, 得到了关于G幂零的几个充要条件和充分条件.     

某些子群的覆盖-远离性质对有限群结构的影响

利用覆盖-远离子群的概念研究了群的超可解性和幂零性.首先利用有限群G的Fitting子群和Sylow子群的覆盖-远离性质给出了关于G超可解的几个充分条件;然后再对G的Sylow子群的正规化子等的覆盖-远离性质进行讨论,得到了关于G幂零的几个充要条件和充分条件.     

有限群的X-ss-半置换子群

给出了X-ss-半置换子群的概念,利用其性质研究它对有限群结构的影响,并利用准素子群的X-ss-半置换性得到了有限群G为p-幂零群的一些充分条件,以及G为p-超可解群的充要条件.     

共轭置换子群对有限群可解性的影响

群G的子群H称为G的共轭置换子群,若HHg=HgH,对任意g∈G都成立。利用共轭置换子群的定义,给出了共轭置换子群的一些性质和有限群成为可解群的六个充分条件,从而推广了文[1]中的部分结果。     

Characterization of MicroRNA~* Species in Peking Duck Skin

A substantial fraction of miRNA* species are conserved in animals and can repress activities of target genes. This study aims to investigate the miRNA* species in duck skin by using Solexa sequencing. We obtained a total of 96 miRNA* species in two skin small RNA libraries and identified 56 miRNA/miRNA* (miR/miR*) pairs. Nucleotide bias of miRNA* indicated that the priority was C>A>U>G for the first nucleotide and U>C>A>G for the last nucleotide. Comparison analyses showed that 3′-U accounted for a higher proportion in the 56 miR/miR* pairs. Among the top 20 expressed miRNA* species, 17 were shared by two libraries and most of the miRNA* species were highly conservative, especially in the "seed region". miR-199a* were expressed highly in our samples, which was also previously shown abundant in mouse hair follicle. Furthermore, four miRNA* species were predicted to target their genes in signal pathways of feather follicle development and feather morphogenesis despite very low levels.     

πc-正规子群对有限群结构的影响

有限群G的子群H称为πx-正规于G,如果存在T(△)G,使得G=HT且H ∩ T≤HGπ,其中π为一些素数的集合,HG为G的包含于H的最大正规π-子群.利用πc-正规子群的一些结论来确定一些群的结构.主要结论是:设G为有限群,N为G的非平凡正规π子群,则N可解当且仅当G的每个不包含N的极大子群πc-正规于G.     

周期FC群的几种Frattini性质

研究了周期FC群的Frattini性质,证明了局部p-幂零性、局部p-可解性和局部p-超可解性是周期FC群类的Frattini性质.     

有限群可解的一个充分条件

证明了如下定理:设G是有限群,π_e(G)是G中元素的阶之集,如果π_e(G)∩{2}=Ф,或π_e(G)∩{3,4}=Ф,或π_e(G)∩{3,5}=Ф,则G可解.进一步,用与π_e(G)的交为空集来判定G可解,仅有上述3种情形.     

极大子群的θ-偶、半正规对群结构的影响

将通过群系定义的极大子群的θ-偶的条件与半正规的条件结合起来刻画群的超可解性.证明了定理3 群G超可解当且仅当对于G的每个极大子群M∈Fu(G),M在G中半正规或者存在一个极大θ-偶(C,D),使得G=MC,且∣C/D∣无平方因子.