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SEMISYMMETRIC CUBIC GRAPHS OF ORDER 34p<sup>3</sup>
Darafsheh, Mohammad Reza,Shahsavaran, Mohsen Korean Mathematical Society 2020 대한수학회보 Vol.57 No.3
A simple graph is called semisymmetric if it is regular and edge transitive but not vertex transitive. Let p be a prime. Folkman proved [J. Folkman, Regular line-symmetric graphs, Journal of Combinatorial Theory 3 (1967), no. 3, 215-232] that no semisymmetric graph of order 2p or 2p<sup>2</sup> exists. In this paper an extension of his result in the case of cubic graphs of order 34p<sup>3</sup>, p ≠ 17, is obtained.
ON NON-ISOMORPHIC GROUPS WITH THE SAME SET OF ORDER COMPONENTS
Darafsheh, Mohammad Reza Korean Mathematical Society 2008 대한수학회지 Vol.45 No.1
In this paper we will prove that the simple groups $B_p(3)\;and\;G_p(3)$, p an odd prime number, are 2-recognizable by the set of their order components. More precisely we will prove that if G is a finite group and OC(G) denotes the set of order components of G, then OC(G) = $OC(B_p(3))$ if and only if $G{\cong}B_p(3)\;or\;C_p(3)$.
CHARACTERIZATION OF THE GROUPS D<sub>p+1</sub>(2) AND D<sub>p+1</sub>(3) USING ORDER COMPONENTS
Darafsheh, Mohammad Reza Korean Mathematical Society 2010 대한수학회지 Vol.47 No.2
In this paper we will prove that the groups $D_{p+1}$(2) and $D_{p+1}$(3), where p is an odd prime number, are uniquely determined by their sets of order components. A main consequence of our result is the validity of Thompson's conjecture for the groups $D_{p+1}$(2) and $D_{p+1}$(3).
THE CHARACTER TABLE OF THE GROUP $GL_2(Q)$WHEN EXTENDED BY A CERTAIN GROUP OF ORDER TWO
Darafsheh, M.R.,Larki, F.Nowroozi 한국전산응용수학회 2000 The Korean journal of computational & applied math Vol.7 No.3
Let G denote either of the groups $GL_2(q)$ or $SL_2(q)$. Then ${\theta}$:G -> G given by ${\theta}(A)$ = ${(A^t)}^{-l}$, where $A^t$ denotes the transpose of the matrix A, is an automorphism of G. Therefore we may form the group G.$<{\theta}>$ which is the split extension of the group G by the cyclic group $<{\theta}>$ of order 2. Our aim in this paper is to find the complex irreducible character table of G.$<{\theta}>$.
EQUIVALENCE CLASSES OF MATRICES IN $GL_2(Q)$ AND $SL_2(Q)$
Darafsheh, M.R.,Larki, F. Nowroozi 한국전산응용수학회 1999 Journal of applied mathematics & informatics Vol.6 No.2
Let G denote either of the groups $GL_2(q)$ or $SL_2(q)$. The mapping $theta$ sending a matrix to its transpose-inverse is an auto-mophism of G and therefore we can form the group $G^+$ = G.<$theta$>. In this paper conjugacy classes of elements in $G^+$ -G are found. These classes are closely related to the congruence classes of invert-ible matrices in G.
A CHARACTERIZATION OF THE GROUP A<sub>22</sub> BY NON-COMMUTING GRAPH
Darafsheh, Mohammad Reza,Yosefzadeh, Pedram Korean Mathematical Society 2013 대한수학회보 Vol.50 No.1
Let G be a finite non-abelian group. We define the non-commuting graph ${\nabla}(G)$ of G as follows: the vertex set of ${\nabla}(G)$ is G-Z(G) and two vertices x and y are adjacent if and only if $xy{\neq}yx$. In this paper we prove that if G is a finite group with $${\nabla}(G){\simeq_-}{\nabla}(\mathbb{A}_{22})$$, then $$G{\simeq_-}\mathbb{A}_{22}$$where $\mathbb{A}_{22}$ is the alternating group of degree 22.
GENERATING PAIRS FOR THE SPORADIC GROUP Ru
Darafsheh, M.R.,Ashrafi, A.R. 한국전산응용수학회 2003 Journal of applied mathematics & informatics Vol.12 No.1
A finite group G is called (l, m, n)-generated, if it is a quotient group of the triangle group T(l, m, n) = 〈$\chi$, y, z│$\chi$$\^$l/ = y$\^$m/ = z$^n$ = $\chi$yz = 1〉. In [19], the question of finding all triples (l, m, n) such that non-abelian finite simple group are (l, m, n)-generated was posed. In this paper we partially answer this question for the sporadic group Ru. In fact, we prove that if p, q and r are prime divisors of │Ru│, where p < q < r and$.$(p, q) $\neq$ (2, 3), then Ru is (p, q, r)-generated.
A CHARACTERIZATION OF GROUPS PSL(3, q) BY THEIR ELEMENT ORDERS FOR CERTAIN q
Darafsheh, M.R.,Karamzadeh, N.S. 한국전산응용수학회 2002 The Korean journal of computational & applied math Vol.9 No.2
Let G be a finite group and $\omega$(G) the set of elements orders of G. Denote by h($\omega$(G)) the number of isomorphism classes of finite groups H satisfying $\omega$(G)=$\omega$(H). In this paper, we show that for G=PSL(3, q), h($\omega$(G))=1 where q=11, 12, 19, 23, 25 and 27 and h($\omega$(G)=2 where q = 17 and 29.
A CHARACTERIZATION OF GROUPS PSL(3,q) BY THEIR ELEMENT ORDERS FOR CERTAIN q
M.R. Darafsheh,N.S. Karamzadeh 한국전산응용수학회 2002 Journal of applied mathematics & informatics Vol.9 No.2
Let G be a finite group and W(G) the set of element orders ofG. Denote by h(W(G)) the number of isomorphism classes offinite groups H satisfying W(G)=W(H). In this paper, we showthat for G=PSL(3,q), h(W(G))=1 where q=11,13,19,23,25 and27 and h(W(G)=2 where q=17 and 29.
CHARACTERIZATION OF THE GROUPS Dp+1(2) AND Dp+1(3) USING ORDER COMPONENTS
Mohammad Reza Darafsheh 대한수학회 2010 대한수학회지 Vol.47 No.2
In this paper we will prove that the groups Dp+1(2) and Dp+1(3), where p is an odd prime number, are uniquely determined by their sets of order components. A main consequence of our result is the validity of Thompson’s conjecture for the groups Dp+1(2) and Dp+1(3).