The probability that the product of two elements of finite group algebra is zero

Let $\mathbb{F}_qG$ be a finite group algebra. We denote by $P(\mathbb{F}_qG)$ the probability that the product of two elements of $\mathbb{F}_qG$ be zero. In this paper, the general formula for computing the $P(\mathbb{F}_qG)$ are established for the cyclic groups $C_n$, the Quaternion group $Q_8$ and the symmetric group $S_3$, for some cases

Genus One Almost Simple Groups of Lie Rank Two

In this paper, we assume that $G$ is a finite group with socle $PSL(3,q)$ and $G$ acts on the projective points of 2-dimensional projective geometry $PG(2,q)$, $q$ is a prime power. By using a new method, we show that $G$ possesses no genus one group if $q>13$. Furthermore, we study the connectedness of the Hurwitz space $\mathcal{H}^{in}_{r}(G)$ for a given group $G$, genus one and $q\leq 13$

Genus One Almost Simple Groups of Lie Rank Two

In this paper, we assume that $G$ is a finite group with socle $PSL(3,q)$ and $G$ acts on the projective points of 2-dimensional projective geometry $PG(2,q)$, $q$ is a prime power. By using a new method, we show that $G$ possesses no genus one group if $q>13$. Furthermore, we study the connectedness of the Hurwitz space $\mathcal{H}^{in}_{r}(G)$ for a given group $G$, genus one and $q\leq 13$

RESIDENTIAL BUILDING DEVELOPMENT PROCESS IN KURDISTAN REGION GOVERNMENT

Nowadays, Residential buildings have become the most important part of real-estate markets in (KRG). The layout of housing in Kurdistan has transformed the face of major cities across the Region. Rapid changes since 2003, have witnessed copious architectural structures and large housing projects that have reshaped the landscape of its cities. The aim of this study is to study the housing developing policy in KRG. The objectives of the study are to evaluate the KRG's housing development policy and to investigate the types of house and the price range preferred by the potential buyer. The study focus on private residential building development projects and it is carried out by questionnaires and interviews. The respondents are the house buyers and the developers. A total of 100 questionnaires were distributed to the respondents and 78 questionnaires were returned duly answered. The data collected is analyzed using the SPSS (Statistical Package for the Social Sciences) and Average Index. The results of research indicated that the KRG’s housing development policy covers the ownership of the project land, full repatriation of project investment and profits allowed, import of spare parts tax exempt up to 15% of project cost and the employment of foreign workers allowed. Moreover, the types of house preferred by the house buyers are of double storey type and to be of corner lot. The price range preferred by the potential buyers are between (40,000 to 100,000) USD

Finite groups of small genus

For a finite group $G$, the Hurwitz space $H$$^i$$_r$$_,$$^n$$_g$ ($G$) is the space of genus $g$ covers of the Riemann sphere with $r$ branch points and the monodromy group $G$. Let ε$_r$($G$) = {($x$$_1$,...,$x$$_r$) : $G$ = $\langle$$x$$_1$,...,$x$$_r$$\rangle$, Π$^r$$_i$$_=$$_1$ $x$$_i$ = 1, $x$$_i$ ϵ $G$#, $i$ = 1,...,$r$}. The connected components of $H$$^i$$_r$$_,$$^n$$_g$($G$) are in bijection with braid orbits on ε$_r$($G$). In this thesis we enumerate the connected components of $H$$^i$$_r$$_,$$^n$$_g$($G$) in the cases where $g$ $\leq$ 2 and $G$ is a primitive affine group. Our approach uses a combination of theoretical and computational tools. To handle the most computationally challenging cases we develop a new algorithm which we call the Projection-Fiber algorithm

Classification of All Primitive Groups of Degrees Four and Five

Let be a compact Riemann surface of genus and be indecomposable meromorphic function of Riemann sphere by . Isomorphisms of such meromorphic functions are in one to one correspondence with conjugacy classes of tuples of permutations in such that and a subgroup of . Our goal of this work is to give a classification in the case where is of genus 1 and the subgroup is a primitive subgroup of or . We present the ramification types for genus 1 to complete such a classification. Furthermore, we show that the subgroups and of do not possesses primitive genus 1 systems

Structure of intersection graphs

 Let G be a finite group and let N be a fixed normal subgroup of G.  In this paper, a new kind of graph on G, namely the intersection graph is defined and studied. We use  to denote this graph, with its vertices are all normal subgroups of G and two distinct vertices are adjacent if their intersection in N. We show some properties of this graph. For instance, the intersection graph is a simple connected with diameter at most two. Furthermore we give the graph structure of  for some finite groups such as the symmetric, dihedral, special linear group, quaternion and cyclic groups. </p

Connected Components of H_(r,g)^A (G)

The Hurwitz space   is the space of genus g covers of the Riemann sphere  with  branch points and the monodromy group . In this paper, we enumerate the connected components of the Hurwitz spaces  for a finite primitive group of degree 7 and genus zero except . We achieve this with the aid of the computer algebra system GAP and the MAPCLASS package

Connected Components of the Hurwitz Space for the Symmetric Group of Degree 7

The Hurwitz space  is the space of genus  covers of the Riemann sphere  with branch points and the monodromy group . Let be the symmetric group . In this paper, we enumerate the connected components of . Our approach uses computational tools, relying on the computer algebra system GAP and the MAPCLASS package, to find the connected components of . This work gives us the complete classification of  primitive genus zero symmetric group of degree seven.