一类无限群中局部幂零性的判定准则

设G是任意群,群G的Frattini子群nat(G)定义为G的所有极大子群的交.类似地,群G的另外两个特征子群nFrat(G)及R(G)分别定义为群G的所有极大正规子群及群G的所有正规的极大子群的交.本文通过对nat(G),nnat(G)及R(G)的相互包含关系的研究,得到CF-群或中心由多重循环群的扩张群中局部幂零性的一个判定准则.同时也讨论了在某些群类中若干种广义幂零性的等价性.     

一类无限群中局部幂零性的判定准则

设G是任意群,群G的Frattini子群Frat(G)定义为G的所有极大子群的交.类似地,群G的另外两个特征子群nFrat(G)及R(G)分别定义为群G的所有极大正规子群及群G的所有正规的极大子群的交.本文通过对Frat(G),nFrat(G)及R(G)的相互包含关系的研究,得到CF-群或中心由多重循环群的扩张群中局部幂零性的一个判定准则.同时也讨论了在某些群类中若干种广义幂零性的等价性.     

LOCAL C-COSINE FAMILY THEORY AND APPLICATION

ＬＯＣＡＬＣ－ＣＯＳＩＮＥＦＡＭＩＬＹＴＨＥＯＲＹＡＮＤＡＰＰＬＩＣＡＴＩＯＮ￥ＨＵＡＮＧＦＡＬＵＮ；ＨＵＡＮＧＴＩＮＧＷＥＮＡｂｓｔｒａｃｔ：ＴｈｉｓｐａｐｅｒｉｎｔｒｏｄｕｃｅｓｔｈｅｃｏｎｃｅｐｔｏｆｌｏｃａｌＣ－ｃｏｓｉｎｅｆａｍｉｌｙａｎｄ...     

关于一类自同构群

本文给出了所有Ｐ＾３阶（ｐ为素数）群的自同构群的结构。     

局部环上辛群在线性群中的扩群

本文完全定出了局部环上辛群在一般线性群中的扩群.     

具有幂零局部子群的有限群

一个有限非幂零群G称为PN-群,如果NC(P)是幂零的,对于每个素数p和每个满足PZ∞(G)的非正规子群p-子群P.本文将给出可解PN-群的结构和一些特征定理.     

局部环上辛群在线性群中的扩群

本文完全定出了局部环上辛群在一般线性群中的扩群.     

ISOTYPE SUBGROUPS OF LOCAL WARFIELD GROUPS

Necessary and sufficient conditions are given for an isotype subgroup H of a p-local Warfield group G to be, itself, Warfield.     

具有幂零局部子群的有限群

一个有限非幂零群G称为PN-群,如果NG(P)是幂零的,对于每个素数p和每个满足P(∈)Z∞(G)的非正规子群p-子群P.本文将给出可解PN-群的结构和一些特征定理.     

对称群上的一类Cayley图的边传递性和Hamilton性

Let Sn be the symmetric group,g+I=(123i),g-I=(1i32) and M+n={g+I:4≤I≤n},then M+n is a minimal generating set of Sn,where n≥5.It is proved that Cayley graph Cay(Sn,M+n∪M-n) is Hamiltonian and edge symmetric.     

弱局部对角占优阵及其在稳定性理论中的应用

引进了弱局部地角占优阵的概念，研究了这类矩阵的性质及其特征值问题，并给出了在稳定性理论中的应用。     

GENERALIZED OPERATORS AND OPERATOR-VALUED DISTRIBUTIONS IN QUANTUM FIELD THEORY

The relation between generalized operators and operator-valued distributions is discussed so that these two viewpoints can be used alternatively to explain quantum fields.     

LOCAL THEORY IN CRITICAL SPACES FOR COMPRESSIBLE VISCOUS AND HEAT-CONDUCTIVE GASES

We are concerned with local existence and uniqueness of solutions for a general model of viscous and heat-conductive gases with low regularity assumptions on the initial data (the velocity and the temperature may be discontinuous). Local well-posedness is showed to hold in spaces which are critical with respect to the scaling of the equations, provided that the initial density is close enough to a positive constant. When initial data are a trifle more regular, local well-posedness holds for any initial density bounded away from zero. This former result lies on new estimates for linear heat equations with a non constant diffusion coefficient.     

一类线性算子的扰动理论及其应用

<正> 离散型算子扰动理论的主要结果为Schwartz—Kramer得到,这可详见[5].[5]中是使用谱族的方法来处理的,我们将用无条件基的理论来证明这个结果(定理1.3的1)2)).显然证明较之[5]大为简化,并且免去了在Banach空间情形吋所要求的“弱完备”条件,以及得到其它一些结果(定理1.3的3)4)).     

APPLICATIONS OF THE THEORY OF CAMINA GROUPS

Thispaperisdividedintofoursections.InSection1,wepresentaconjugacy-classversionofCaminaHypotheses.InSection2,wegivesomebasicfactsaboutaCaminagroupGwiththekernelG',whichwillbeusedinSections3and4.InSections3and4,weapplytheCaminagrouptheorytodiscussingtw...     

SPECIAL REDUCTIVE GROUPS OVER AN ARBITRARY FIELD

A linear algebraic group G defined over a field k is called special if every G-torsor over every field extension of k is trivial. In 1958 Grothendieck classified special groups in the case where the base field is algebraically closed. In this paper we describe the derived subgroup and the coradical of a special reductive group over an arbitrary field k. We also classify special semisimple groups, special reductive groups of inner type, and special quasisplit reductive groups over an arbitrary field k. Finally, we give an application to a conjecture of Serre.     

LOCAL ESTIMATE ABOUT SCHRODINGER MAXIMAL OPERATOR ON H-TYPE GROUPS

Let ? be full Laplacian on H-type group G. Then for every compact set D ■ G,a local estimate of the Schr¨odinger maximal operator holds, that is, ∫_(D)sup |e~(it?)f(x)|~2dx ■||f ||_(H~s)~2, s 1/2.We also show that the above inequality fails when s 1/4.     

THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK POSITIVE SOLUTIONS TO A CLASS OF KIRCHHOFF EQUATION

In the present paper, we consider the nonlocal Kirchhoff problem ■,where a, b 0, 1 p 5 and ■ 0 is a parameter. Under some assumptions on Q(x),we show the existence and local uniqueness of positive multi-peak solutions by LyapunovSchmidt reduction method and the local Pohozaev identity method, respectly.     

THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK SOLUTIONS TO A CLASS OF KIRCHHOFF TYPE EQUATIONS

In this paper, we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations -(ε²a + εb∫_R³|?u|²)?u + V(x)u = u^p, u > 0 in R³,which concentrate at non-degenerate critical points of the potential function V(x), where a, b >0, 1 < p < 5 are constants, and ε > 0 is a parameter. Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity, we establish the existe...