**Volume 09 (2020)**

**Volume 08 (2019)**

**Volume 07 (2018)**

**Volume 06 (2017)**

**Volume 05 (2016)**

**Volume 04 (2015)**

**Volume 03 (2014)**

**Volume 02 (2013)**

**Volume 01 (2012)**

# Main Subjects = Group theory and generalizations
Number of Articles: 16

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

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

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**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 ...
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##### 2. A representation for some groups, a geometric approach

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

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

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

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

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

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**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 $\Gamma(H)=\Gamma(G)$, ...
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##### 5. On the irreducibility of the complex specialization of the representation of the Hecke algebra of the complex reflection group $G_7$

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

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**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 ...
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##### 6. On categories of merotopic, nearness, and filter algebras

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

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**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 ...
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##### 7. On $m^{th}$-autocommutator subgroup of finite abelian groups

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

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**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 ...
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##### 8. Recognition by prime graph of the almost simple group PGL(2, 25)

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

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**Abstract **

Throughout this paper, every groups are finite. The prime graph of a group $G$ is denoted by $\Gamma(G)$. Also $G$ is called recognizable by prime graph if for every finite 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 ...
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##### 9. Probability of having $n^{th}$-roots and n-centrality of two classes of groups

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

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**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, ...
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##### 10. Quotient Arens regularity of $L^1(G)$

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

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**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 ...
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##### 11. Characterization of $G_2(q)$, where $2 < q \equiv 1(mod\ 3)$ by order components

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

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**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 finite group with $OC(G)=OC(G_2(q))$, then $G$ is isomorphic to $G_2(q)$.
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##### 12. OD-characterization of $U_3(9)$ and its group of automorphisms

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

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**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 ...
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##### 13. Module amenability and module biprojectivity of θ-Lau product of Banach algebras

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

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**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 ...
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##### 14. OD-characterization of $S_4(4)$ and its group of automorphisms

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

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**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, ...
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##### 15. On the Finite Groupoid G(n)

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

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**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) ...
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##### 16. Some results of semilocally simply connected property

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