##### Volume 01 (2012)
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

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

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)

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