Group theory and generalizations
1. Irreducibility of the tensor product of Albeverio's representations of the Braid groups $B_3$ and $B_4$

A. Taha; M. N. Abdulrahim

Volume 08, Issue 02 , Spring 2019, , Pages 105-115

Abstract
  ‎We consider Albeverio's linear representations of the braid groups $B_3$ and $B_4$‎. ‎We specialize the indeterminates used in defining these representations to non zero complex numbers‎. ‎We then consider the tensor products of the representations of $B_3$ and the tensor products ...  Read More

Group theory and generalizations
2. A representation for some groups, a geometric approach

A. Parsian

Volume 07, Issue 02 , Spring 2018, , Pages 149-153

Abstract
  ‎In the present paper‎, ‎we are going to use geometric and topological concepts‎, ‎entities and properties of the‎ ‎integral curves of linear vector fields‎, ‎and the theory of differential equations‎, ‎to establish a representation for some groups ...  Read More

Combinatorics
3. On Laplacian energy of non-commuting graphs of finite groups

P. Dutta; R. K. Nath

Volume 07, Issue 02 , Spring 2018, , Pages 121-132

Abstract
  ‎Let $G$ be a finite non-abelian group with center $Z(G)$‎. ‎The non-commuting graph of $G$ is a simple undirected graph whose vertex set is $G\setminus Z(G)$ and two vertices $x$ and $y$ are adjacent if and only if $xy \ne yx$‎. ‎In this paper‎, we compute Laplacian energy of ...  Read More

Group theory and generalizations
4. On some Frobenius groups with the same prime graph as the almost simple group ${ {\bf PGL(2,49)}}$

A. Mahmoudifar

Volume 06, Issue 03 , Summer 2017, , Pages 217-221

Abstract
  The prime graph of a finite group $G$ is denoted by $\Gamma(G)$ whose vertex set is $\pi(G)$ and two distinct primes $p$ and $q$ are adjacent in $\Gamma(G)$, whenever $G$ contains an element with order $pq$. We say that $G$ is unrecognizable by prime graph if there is a finite group $H$ with $\Gamma(H)=\Gamma(G)$, ...  Read More

Group theory and generalizations
5. On the irreducibility of the complex specialization of the representation of the Hecke algebra of the complex reflection group $G_7$

M. Y. Chreif; M. Abdulrahim

Volume 05, Issue 04 , Autumn 2016, , Pages 263-270

Abstract
  We consider a 2-dimensional representation of the Hecke algebra $H(G_7, u)$, where $G_7$ is the complex reflection group and $u$ is the set of indeterminates $u = (x_1,x_2,y_1,y_2,y_3,z_1,z_2,z_3)$. After specializing the indetrminates to non zero complex numbers, we then determine a necessary ...  Read More

Group theory and generalizations
6. On categories of merotopic, nearness, and filter algebras

V. Gompa

Volume 05, Issue 02 , Spring 2016, , Pages 111-118

Abstract
  We study algebraic properties of categories of Merotopic, Nearness, and Filter Algebras. We show that the category of filter torsion free abelian groups is an epireflective subcategory of the category of filter abelian groups. The forgetful functor from the category of filter rings to filter monoids ...  Read More

Group theory and generalizations
7. On $m^{th}$-autocommutator subgroup of finite abelian groups

A. Gholamian; M. M. Nasrabadi

Volume 05, Issue 02 , Spring 2016, , Pages 135-144

Abstract
  Let $G$ be a group and $Aut(G)$ be the group of automorphisms of‎ ‎$G$‎. ‎For any natural‎ number $m$‎, ‎the $m^{th}$-autocommutator subgroup of $G$ is defined‎ ‎as‎: ‎$$K_{m} (G)=\langle[g,\alpha_{1},\ldots,\alpha_{m}] |g\in G‎,\‎alpha_{1},ldots,\alpha_{m}\in ...  Read More

Group theory and generalizations
8. Recognition by prime graph of the almost simple group PGL(2, 25)

A. Mahmoudifar

Volume 05, Issue 01 , Winter 2016, , Pages 63-66

Abstract
  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 $G\cong H$. Until now, it is proved that if $k$ is an odd number and ...  Read More

Group theory and generalizations
9. Probability of having $n^{th}$-roots and n-centrality of two classes of groups

M. Hashemi; M. Polkouei

Volume 05, Issue 01 , Winter 2016, , Pages 55-62

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

Group theory and generalizations
10. Quotient Arens regularity of $L^1(G)$

A. Zivari-Kazempour

Volume 04, Issue 04 , Autumn 2015, , Pages 275-281

Abstract
  Let $\mathcal{A}$ be a Banach algebra with BAI and $E$ be an introverted subspace of $\mathcal{A}^\prime$. In this paper we study the quotient Arens regularity of $\mathcal{A}$ with respect to $E$ and prove that the group algebra $L^1(G)$ for a locally compact group $G$, is quotient Arens regular ...  Read More

Group theory and generalizations
11. Characterization of $G_2(q)$, where $2 < q \equiv 1(mod\ 3)$ by order components

P. Nosratpour

Volume 04, Issue 01 , Winter 2015, , Pages 11-23

Abstract
  In this paper we will prove that the simple group $G_2(q)$, where $2 < q \equiv 1(mod3)$ is recognizable by the set of its order components, also other word we prove that if $G$ is a fi nite group with $OC(G)=OC(G_2(q))$, then $G$ is isomorphic to $G_2(q)$.  Read More

Group theory and generalizations
12. OD-characterization of $U_3(9)$ and its group of automorphisms

P. Nosratpour

Volume 03, Issue 04 , Autumn 2014, , Pages 205-209

Abstract
  Let $L = U_3(9)$ be the simple projective unitary group in dimension 3 over a field  with 92 elements. In this article, we classify groups with the same order and degree pattern as an almost simple group related to $L$. Since $Aut(L)\equiv Z_4$ hence almost simple groups related to $L$ are ...  Read More

Group theory and generalizations
13. Module amenability and module biprojectivity of θ-Lau product of Banach algebras

D. Ebrahimi Bagha; H. Azaraien

Volume 03, Issue 03 , Summer 2014, , Pages 185-196

Abstract
  In this paper we study the relation between module amenability of $\theta$-Lau product $A×_\theta B$ and that of Banach algebras $A, B$. We also discuss module biprojectivity of $A×\theta B$. As a consequent we will see that for an inverse semigroup $S$, $l^1(S)×_\theta l^1(S)$ is module ...  Read More

Group theory and generalizations
14. OD-characterization of $S_4(4)$ and its group of automorphisms

P. Nosratpour

Volume 02, Issue 03 , Summer 2013, , Pages 161-166

Abstract
  Let $G$ be a finite group and $\pi(G)$ be the set of all prime divisors of $|G|$. The prime graph of $G$ is a simple graph $\Gamma(G)$ with vertex set $\pi(G)$ and two distinct vertices $p$ and $q$ in $\pi(G)$ are adjacent by an edge if an only if $G$ has an element of order $pq$. In this case, ...  Read More

Group theory and generalizations
15. On the Finite Groupoid G(n)

M. Azadi; H. Amadi

Volume 02, Issue 03 , Summer 2013, , Pages 153-159

Abstract
  In this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid G(n). Also we show that G(n) contains commuting regular subsemigroup and give a necessary and sufficient condition for the groupoid G(n) ...  Read More

Group theory and generalizations
16. Some results of semilocally simply connected property

A. Etemad Dehkordya; M. Malek Mohamad

Volume 02, Issue 03 , Summer 2013, , Pages 137-143

Abstract
  If we consider some special conditions, we can assume fundamental group of a topological space as a new topological space. In this paper, we will present a number of theorems in topological fundamental group related to semilocally simply connected property for a topological space.  Read More