Locally Nilpotent Groups with Weak Conditions of π-Layer Minimality and π-Layer Maximality

We investigate locally nilpotent groups with weak conditions of -layer minimality and -layer maximality.     

On Inner π’—closed Groups with Operator Groups

1.IntroductionandStatementofMainResultsLetKbeasetOfPrimesandK'thecomplementarysetofK.LetGbeafinitegroupandAanon-identitygroupofautomophismsofGsuchthat(lAI,lGI)=1.AsiswellknownitisoftentoobtainonthestructureofGifweimposesomeconditiononproperA-invariantsub-groupsofG.Inthispaper,weareinterestedinthefollowingproblem:IfeveryproperA-in-variantsubgroupsofGisK,closedbutGitselfisnot,thatis,GisaninnerK,closedgroupwithoperatorA,whatisthestructureofG?ThespecialcasethatK={p}wassettledbyProfesso…     

Groups with π-maximal and π-layer maximal conditions

By analogy with π-minimal, π-layer minimal, primary minimal, and layer minimal conditions, similar maximal conditions are introduced and studied. Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 311–320, August, 2000.     

Groups with π-Minimal and π-Layer Minimal Conditions. II

For an arbitrary set of prime numbers we study the properties and structure of groups satisfying the -minimal and -layer minimal conditions. In particular, we describe the structure of the almost RN-groups (and thereby that of the locally solvable groups) with these conditions. Under the assumption 2, we describe the structure of locally graded groups (and thereby that of locally finite groups) with these conditions.     

Groups with π-Minimal and π-Layer Minimal Conditions. I

Siberian Mathematical Journal -     

Groups with π-Minimal and π-Layer Minimal Conditions. II

For an arbitrary set π of prime numbers we study the properties and structure of groups satisfying the π-minimal and π-layer minimal conditions. In particular, we describe the structure of the almost RN-groups (and thereby that of the locally solvable groups) with these conditions. Under the assumption 2∈π, we describe the structure of locally graded groups (and thereby that of locally finite groups) with these conditions.     

On Strong π-Regularity and π-Regularity

Rowen showed that the 2 by 2 full matrix rings over strongly π-regular rings need not be strongly π-regular. In this note we extend Rowen's method to the n by n full matrix rings. Moreover we show that the n by n full matrix rings over π-regular rings need not be π-regular.     

On Hardy’s Uncertainty Principle for Solvable Locally Compact Groups

We establish analogues of Hardy’s uncertainty principle for the Fourier transform on ? for locally compact Abelian groups and for some classes of solvable Lie groups, such as diamond groups and exponential Lie groups with non-trivial centre.     

On Subgroups and Quotient Groups of L-fuzzy Topological Groups

In paper [1], it gave the concept and basic properties of L-fuzzy topological groups. This paper will enter the concept of quotient groups of L-fuzzy topological groups and will prove some properties of subgroups and quotient groups. The persent work is the continuation of [1] and hence all the conventions in [1] still hold good in the present paper.     

On Factorization of Entire Functions with Finite Deficient Values

Following Gross we say that a meromorphic function F(z)has a factoriza- tion with left factor f(z)and right factor g(z),if     

On Pointwise Uniform and Locally Uniform Spaces

ＯｎＰｏｉｎｔｗｉｓｅＵｎｉｆｏｒｍａｎｄＬｏｃａｌｌｙＵｎｉｆｏｒｍＳｐａｃｅｓＧａｏＹｕｎｐｅｎｇ（高云鹏）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨａｒｂｉｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｈａｒｂｉｎ，Ｈａｒｂｉｎ，１５０００１）...     

Finite π-Quasisurpersolvable Groups

Ｆｉｎｉｔｅπ－ＱｕａｓｉｓｕｒｐｅｒｓｏｌｖａｂｌｅＧｒｏｕｐｓＹｕＹｕｅｈｕａ（于越华）（ＩｎｓｔｉｔｕｔｅｏｆＩｎｆｏｒｍａｔｉｏｎａｌＥｎｇｉｎｅｅｒｉｎｇ，Ｚｈｅｎｇｚｈｏｕ４５０００２）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒｗｅｈａｖｅ...     

On the Product and Factorization of Lattice Implication Algebras

In this paper,the concepts of product and factorization of lattice implication algebra areproposed,the relation between lattice implication product algebra and its factors and some properties oflattice implication product algebras are discussed.     

On Finite Groups with Some Semi Cover-Avoiding Subgroups

A subgroup H of a finite group G is said to have the semi-cover-avoiding property in G if there is a chief series of G such that H covers or avoids every chief factor of the series. In this paper, some new results are obtained based on the assumption that some subgroups have the semi-cover-avoiding property in the group.     

On p-Radical Groups

Ｏｎｐ－ＲａｄｉｃａｌＧｒｏｕｐｓ￥ＺｈｏｕＹｏｎｇｘｉｎ（周永新）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｅｂｅｉＴｅａｃｈｅｒｓＵｎｉｖｅｒｓｉｔｙ，Ｓｈｉｊｉａｚｈｕａｎｇ，Ｈｅｂｅｉ，０５００１６）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐ...     

On C.R. Rao’s Theorem for Locally Compact Abelian Groups

Doklady Mathematics - Let ξ 1, ξ2, ξ3 be independent random variables with values in a locally compact Abelian group X with nonvanishing characteristic functions, and aj, bj be...     

On the Locally Symmetric and Cosympectic Bochner Flat Manifolds

ＯｎｔｈｅＬｏｃａｌｌｙＳｙｍｍｅｔｒｉｃａｎｄＣｏｓｙｍｐｅｃｔｉｃＢｏｃｈｎｅｒＦｌａｔＭａｎｉｆｏｌｄｓＱｕＣｈｅｎｇｑｉｎ（瞿成勤）（Ｎａｖａｌ．ＥｌｅｃｔｒｏｎｉｃＥｎｇｉｎｅｅｒｉｎｇＣｏｌｌｅｇｅ，Ｎａｎｊｉｎｇ，２１１８００）Ｏｕｙａ...     

On π-Subpairs of π-Blocks

Alperin and Broug have given the p-subpairs in a finite group, and proved that there is a Sylow theorem for p-subpairs. For a π-separable group with π-Hall subgroup nilpotent, we prove that there is a π-Sylow theorem for π-subpairs. Note that our π-subpairs are different from what Robinson and Staszewski gave.     

On n-Dimensional Matrix Groups

An n×matrix A={a_(ij)} will be called a 2-dimensional matrix of order n. We shall study groups of 2m -dimensional matrices of order n over a field of characteristic O with respect to an associative matrix product and we obtain the dimensions of such matrix groups.     

On π-Semicommutative Rings

A ring R is said to be π-semicommutative if a, b ∈ R satisfy ab = 0 then there exists a positive integer n such that anRbn= 0. We study the properties of π-semicommutative rings and the relationship between such rings and other related rings. In particular, we answer a question on left GWZI rings negatively.