2016
4
1
0
0
ON RELATIVE CENTRAL EXTENSIONS AND COVERING PAIRS
2
2
Let (G;N) be a pair of groups. In this article, first we construct a relative central extension for the pair (G;N) such that specialtypes of covering pair of (G;N) are homomorphic image of it. Second, weshow that every perfect pair admits at least one covering pair. Finally,among extending some properties of perfect groups to perfect pairs, wecharacterize covering pairs of a perfect pair (G;N) under some extraassumptions.
1

1
13


A.
Pourmirzaei
Department of Mathematics, Hakim Sabzevari University, P. O. Box 9617976487,
Sabzevar, Iran
Department of Mathematics, Hakim Sabzevari
Iran
a.pmirzaei@gmail.com


M.
Hassanzadeh
Department of Mathematics, Department of Mathematics, Ferdowsi University of
Mashhad, P.O.Box 115991775, Mashhad, Iran.
Department of Mathematics, Department of
Iran
mtr.hassanzadeh@gmail.com


B.
Mashayekhy
Department of Mathematics, Center of Excellence in Analysis on Algebraic Struc
tures, Ferdowsi University of Mashhad, P.O.Box 115991775, Mashhad, Iran.
Department of Mathematics, Center of Excellence
Iran
bmashayekhyf@yahoo.com
Pair of groups
Covering pair
Relative central extension
Isoclinism of pairs of groups
SOME REMARKS ON GENERALIZATIONS OF MULTIPLICATIVELY CLOSED SUBSETS
2
2
Let R be a commutative ring with identity and Mbe a unitary Rmodule. In this paper we generalize the conceptmultiplicatively closed subset of R and we study some propertiesof these genaralized subsets of M. Among the many results in thispaper, we generalize some wellknown theorems about multiplicativelyclosed subsets of R to these generalized subsets of M. Alsowe show that some other wellknown results about multiplicativelyclosed subsets of R are not valid for these generalized subsets ofM.
1

15
27


M.
Ebrahimpour
Department of Mathematics, Faculty of Sciences, ValieAsr University of Rafsanjan
, P.O.Box 518, Rafsanjan, Iran
Department of Mathematics, Faculty of Sciences,
Iran
m.ebrahimpour@vru.ac.ir
Multiplication module
Multiplicatively closed subset of R
(n
ON FINITE GROUPS IN WHICH SSSEMIPERMUTABILITY IS A TRANSITIVE RELATION
2
2
Let H be a subgroup of a finite group G. We say that H is SSsemipermutable in Gif H has a supplement K in G such that H permutes with every Sylow subgroup X of Kwith (jXj; jHj) = 1. In this paper, the Structure of SSsemipermutable subgroups, and finitegroups in which SSsemipermutability is a transitive relation are described. It is shown thata finite solvable group G is a PSTgroup if and only if whenever H K are two psubgroupsof G, H is SSsemipermutable in NG(K).
1

29
36


S.E.
Mirdamadi
Department of Mathematics, University of Shahrekord, P.O.Box 115, Shahrekord,
Iran.
Department of Mathematics, University of
Iran
ebrahimmirdamadi@stu.sku.ac.ir


Gh.R
Rezaeezadeh
Department of Mathematics, University of Shahrekord, P.O.Box 115, Shahrekord,
Iran.
Department of Mathematics, University of
Iran
gh.rezaeezadeh@yahoo.com
SSsemipermutable subgroups
Ssemipermutable subgroups
PSTgroups
ON COMPOSITION FACTORS OF A GROUP WITH THE SAME PRIME GRAPH AS Ln(5)
2
2
The prime graph of a finite group $G$ is denoted by$ga(G)$. A nonabelian simple group $G$ is called quasirecognizable by primegraph, if for every finite group $H$, where $ga(H)=ga(G)$, thereexists a nonabelian composition factor of $H$ which is isomorphic to$G$. Until now, it is proved that some finite linear simple groups arequasirecognizable by prime graph, for instance, the linear groups $L_n(2)$ and $L_n(3)$ are quasirecognizable by prime graph. In this paper, we consider thequasirecognition by prime graph of the simple group $L_n(5)$.
1

37
51


A.
Mahmoudifar
Department of Mathematics, Tehran North Branch, Islamic Azad University, Tehran,
IRAN.
Department of Mathematics, Tehran North Branch,
Iran
alimahmoudifar@gmail.com
projective special linear group
prime graph
element order
STRONGLY DUO AND COMULTIPLICATION MODULES
2
2
Let R be a commutative ring. An Rmodule M is called comultiplication provided that foreach submodule N of M there exists an ideal I of R such that N = (0 : I). In this paper weshow that comultiplication modules are a generalization of strongly duo modules. Uniserialmodules of finite length and hence valuation Artinian rings are some distinguished classes ofcomultiplication rings. In addition, if R is a Noetherian ring, then R is a strongly duoring if and only if R is a comultiplication ring. We also show that Jsemisimple strongly duorings are precisely semisimple rings. Moreover, if R is a perfect ring, then uniserial Rmodules are comultiplication of finite length modules. Finally, we showthat Abelian comultiplication groups are reduced and comultiplication Zmodules(Abeliangroups)are characterized.
1

53
64


S.
Safaeeyan
Department of Mathematics, University of Yasouj , P.O.Box 75914, Yasouj, IRAN.
Department of Mathematics, University of
Iran
safaeeyan@mail.yu.ac.ir
Comultiplication modules
strongly duo modules
Abelian Groups
SIGNED ROMAN DOMINATION NUMBER AND JOIN OF GRAPHS
2
2
In this paper we study the signed Roman dominationnumber of the join of graphs. Specially, we determine it for thejoin of cycles, wheels, fans and friendship graphs.
1

65
77


A.
Behtoei
Department of Mathematics, Imam Khomeini International University, P.O.Box
3414916818, Qazvin, Iran.
Department of Mathematics, Imam Khomeini
Iran
a.behtoei@sci.ikiu.ac.ir


E.
Vatandoost
Department of Mathematics, Imam Khomeini International University, P.O.Box
3414916818, Qazvin, Iran.
Department of Mathematics, Imam Khomeini
Iran
evatandoost@ikiu.ac.ir


F.
Azizi Rajol Abad
Department of Mathematics, Imam Khomeini International University, P.O.Box
3414916818, Qazvin, Iran.
Department of Mathematics, Imam Khomeini
Iran
Signed Roman domination
Join
Cycle
Wheel
Friendship
ARTINIANNESS OF COMPOSED LOCAL COHOMOLOGY MODULES
2
2
Let $R$ be a commutative Noetherian ring and let $fa$, $fb$ be two ideals of $R$ such that $R/({fa+fb})$ is Artinian. Let $M$, $N$ be two finitely generated $R$modules. We prove that $H_{fb}^j(H_{fa}^t(M,N))$ is Artinian for $j=0,1$, where $t=inf{iin{mathbb{N}_0}: H_{fa}^i(M,N)$ is not finitelygenerated $}$. Also, we prove that if $DimSupp(H_{fa}^i(M,N))leq 2$, then $H_{fb}^1(H_{fa}^i(M,N))$ is Artinian for all $i$. Moreover, we show that if $dim N=d$, then $H_{fb}^j(H_{fa}^{d1}(N))$ is Artinian for all $jgeq 1$.
1

79
84


H.
Saremi
Department of Mathematics, Sanandaj Branch, University Islamic Azad University,
Sanandaj, Iran.
Department of Mathematics, Sanandaj Branch,
Iran
hero.saremi@gmail.com
Generalized local cohomology
Local cohomology
Artinian modules