On ℳ p -Supplemented Subgroups of Finite Groups

A subgroup H of G is called ? _p -supplemented in G if there exists a subgroup B of G such that G = HB and TB < G for every maximal subgroup T of H with |H: T| =p ^α. In this paper, we investigate the influence of ? _p -supplemented subgroup and some conditions for p-nilpotency and p-supersolvability of finite groups are obtained.     

On Π-Supplemented Subgroups of a Finite Group

A subgroup H of a finite group G is said to satisfy Π-property in G if for every chief factor L/K of G, |G/K: N_G/K(HK/K ∩ L/K)| is a π(HK/K ∩ L/K)-number. A subgroup H of G is called Π-supplemented in G if there exists a subgroup T of G such that G = HT and H ∩ T ≤ I ≤ H, where I satisfies Π-property in G. In this article, we investigate the structure of a finite group G under the assumption that some primary subgroups of G are Π-supplemented in G. The main result we proved improves a large number of earlier results.     

Some Properties of Divisible and Pure Fuzzy Subgroups

In [3] F. I. Sidky & M. Atif Mishref introduce the concepts of divisible and pure fuzzy subgroups and prove some of their properties. In this paper we further prove following results: Let f: G→G' be an isomorphism of groups and A' be a divisible (pure) fuzzy subgroup of G' under Min, then f~(-1) (A') is a divisible (pure) fuzzy subgroup of G; Let B be a divisible fuzzy subgroup of divisible subgroup H of group G, G=H(?)H', then there exists a fuzzy subgroup B' of H' such that B+B'=A is a fuzzy subgroup of G; If G is a divisible cyclic group, then G is finite group; If A is a fuzzy subgroup of divisible cyclic group, then A is trivial; suppose group G=G_1×G_2×…×G_m, G_i is a divisible cyclic subgroup of G, i=1, 2, …, m, A is a divsiible (pure) fuzzy subgroup of G under Min, then A is trivial.     

On Coflat Modules and Their Hereditary Properties

In[4]Hiremath introduced the notion of copureness in the category of R-modules.We define on this basis coflatness of modules and study some of theirhereditary properties dual to that of the flat modules.The later can be used tocharacterize a class of rings larger than that of semihereditary ones.     

Some Properties of Quasi-keep-range Operators and Their Applications

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Finite Groups With Small Automizers for Their Nonabelian Subgroups

Ｔｈｒｏｕｇｈｏｕｔｔｈｉｓｐａｐｅｒ，Ｇｉｓａｆｉｎｉｔｅｇｒｏｕｐ．ＳｅｔＡｕｔＧ（Ｈ）＝ＮＧ（Ｈ）／ＣＧ（Ｈ）ｆｏｒＨ≤Ｇ．Ｉｎ［ＤＭ］，ａｕｔｈｏｒｓｇａｖｅｔｈｅｆｏｌｏｗｉｎｇｄｅｆｉｎｉｔｉｏｎｓ：（１）ＬｅｔＨ≤Ｇ，ＡｕｔＧ（Ｈ）＝Ｎ...     

A Class of Orbital Cpntractive Principle and Their Equivalence Properties

In this paper, we first establish some necessary and sufficient conditions for a clas(?) of orbital contractive mappings to possess a fixed point, especially, some Rhoades' open questions [1] are answered. Then we study the topological equivalence propetties among orbital contractive mapping, Banach's contractive mapping and Edelstein's contractive mapping. Our results in this paper improve and extend some main results in [1-5].     

Properties of a Subclass of Avakumović Functions and Their Generalized Inverses

We study properties of a subclass of ORV functions introduced by Avakumovi and provide their applications for the strong law of large numbers for renewal processes.     

Theta Subgroups and the Solvability of FiniteGroups

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Schemes for Generating Different Nonlinear Schrödinger Integrable Equations and Their Some Properties

Acta Mathematicae Applicatae Sinica, English Series - In the paper, we want to derive a few of nonlinear Schrödinger equations with various formats and investigate their properties, such as...     

Finite Groups with Only s-quasinormal and Abnormal Subgroups

The concept of an abnormal subgroup of a group G is, in a sense, opposite of thatof a normal subgroup of G. In [J. Algebra, 28(1974), 15-19) Fattahi studied those finitegroups in which each subgroup is either normal or abnormal and characterized all suchgroups. In this paper, as a generalization of Fattahi's result, we study more general groups,i. e., groups with only s-quasinormal and abnormal subgroups and characterize all suchgroups. Morever, some interesting conclusions are also obtained.     

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.     

Essential Subgroups of group

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Free and Non-Free Subgroups of the Group UT(∞, ℤ)

We provide a method to find free groups of rank two in the group of infinite unitriangular matrices. Our groups are generated by two block-diagonal matrices, namely of the form A = diag(C, C, C…), B = diag(I _t , C, C…), where C is a matrix of finite dimension.

We give a necessary and sufficient condition for A and B defined above to generate a free group when C is a transvection. We formulate a sufficient condition to generate a free group, when C is a product of any number of commuting transvections.

We provide a classification of groups defined above, when C is of degree 3 or 4.