Journal of Linear and Topological Algebra
Volume:5 Issue: 1, Winter 2016

This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also, by using Mountain Pass Lemma, we establish the existence of at least one solution with positive energy.

In addition to exploring constructions and properties of limits and colimits in categories of topological algebras, we study special subcategories of topological algebras and their properties. In particular, under certain conditions, reflective subcategories when paired with topological structures give rise to reflective subcategories and epireflective subcategories give rise to epireflective subcategories.

In this paper we consider the so called a vector metric space, which is a generalization of metric space, where the metric is Riesz space valued. We prove some common fixed point theorems for three mappings in this space. Obtained results extend and generalize well-known comparable results in the literature.

In this study, we investigate the further properties of quasi irresolute topological groups defined in [20]. We show that if a group homomorphism f between quasi irresolute topological groups is irresolute at $e_G$, then $f$ is irresolute on $G$. Later we prove that in a semi-connected quasi irresolute topological group $(G,*,tau )$, if $V$ is any symmetric semi-open neighborhood of $e_G$, then $G$ is generated by $V$. Moreover it is proven that a subgroup $H$ of a quasi irresolute topological group $(G,*,tau)$ is semi-discrete if and only if it has a semi-isolated point.

The purpose of this paper is to introduce the concept of pairwise F-closedness in bitopological spaces. This space contains both of pairwise strongcompactness and pairwise S-closedness and contained in pairwise quasi H-closedness. The characteristics and relationships concerning this new class of spaces with other corresponding types are established. Moreover, several of its basic and important properties are discussed.

In this paper, we consider the finitely 2-generated groups $K(s,l)$ and $G_m$ as follows:$$K(s,l)=langle a,b|ab^s=b^la, ba^s=a^lbrangle,\G_m=langle a,b|a^m=b^m=1, {[a,b]}^a=[a,b], {[a,b]}^b=[a,b]rangle$$ and find the explicit formulas for the probability of having nth-roots for them. Also, we investigate integers n for which, these groups are n-central.

Throughout this paper, every groups are finite. The prime graph of a group $G$ is denoted by $Gamma(G)$. Also $G$ is called recognizable by prime graph if for every finite group $H$ with $Gamma(H) = Gamma(G)$, we conclude that $Gcong H$. Until now, it is proved that if $k$ is an odd number and $p$ is an odd prime number, then $PGL(2,p^k)$ is recognizable by prime graph. So if $k$ is even, the recognition by prime graph of $PGL(2,p^k)$, where $p$ is an odd prime number, is an open problem. In this paper, we generalize this result and we prove that the almost simple group $PGL(2,25)$ is recognizable by prime graph.