Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
4
1
2016
09
01
ON RELATIVE CENTRAL EXTENSIONS AND COVERING PAIRS
1
13
EN
A.
Pourmirzaei
Department of Mathematics, Hakim Sabzevari University, P. O. Box 96179-76487,
Sabzevar, Iran
a.pmirzaei@gmail.com
M.
Hassanzadeh
Department of Mathematics, Department of Mathematics, Ferdowsi University of
Mashhad, P.O.Box 1159-91775, Mashhad, 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 1159-91775, Mashhad, Iran.
bmashayekhyf@yahoo.com
10.22044/jas.2016.724
Let (G;N) be a pair of groups. In this article, first we con-struct 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.
Pair of groups,Covering pair,Relative central extension,Isoclinism of pairs of groups
http://jas.shahroodut.ac.ir/article_724.html
http://jas.shahroodut.ac.ir/article_724_70e8def60b0539607f4789672c9b8d32.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
4
1
2016
09
01
SOME REMARKS ON GENERALIZATIONS OF MULTIPLICATIVELY CLOSED SUBSETS
15
27
EN
M.
Ebrahimpour
Department of Mathematics, Faculty of Sciences, Vali-e-Asr University of Rafsanjan
, P.O.Box 518, Rafsanjan, Iran
m.ebrahimpour@vru.ac.ir
10.22044/jas.2016.725
Let R be a commutative ring with identity and Mbe a unitary R-module. 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 well-known theorems about multiplicativelyclosed subsets of R to these generalized subsets of M. Alsowe show that some other well-known results about multiplicativelyclosed subsets of R are not valid for these generalized subsets ofM.
Multiplication module,Multiplicatively closed subset of R,(n
http://jas.shahroodut.ac.ir/article_725.html
http://jas.shahroodut.ac.ir/article_725_cb149f0b8733858d64345565c0ffefb6.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
4
1
2016
09
01
ON FINITE GROUPS IN WHICH SS-SEMIPERMUTABILITY IS A TRANSITIVE RELATION
29
36
EN
S.E.
Mirdamadi
Department of Mathematics, University of Shahrekord, P.O.Box 115, Shahrekord,
Iran.
ebrahimmirdamadi@stu.sku.ac.ir
Gh.R
Rezaeezadeh
Department of Mathematics, University of Shahrekord, P.O.Box 115, Shahrekord,
Iran.
gh.rezaeezadeh@yahoo.com
10.22044/jas.2016.726
Let H be a subgroup of a finite group G. We say that H is SS-semipermutable 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 SS-semipermutable subgroups, and finitegroups in which SS-semipermutability is a transitive relation are described. It is shown thata finite solvable group G is a PST-group if and only if whenever H K are two p-subgroupsof G, H is SS-semipermutable in NG(K).
SS-semipermutable subgroups,S-semipermutable subgroups,PST-groups
http://jas.shahroodut.ac.ir/article_726.html
http://jas.shahroodut.ac.ir/article_726_4dada44a60bbc33404cb7f7dcf783e40.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
4
1
2016
09
01
ON COMPOSITION FACTORS OF A GROUP WITH THE SAME PRIME GRAPH AS Ln(5)
37
51
EN
A.
Mahmoudifar
Department of Mathematics, Tehran North Branch, Islamic Azad University, Tehran,
IRAN.
alimahmoudifar@gmail.com
10.22044/jas.2016.727
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 $L_n(5)$.
projective special linear group,prime graph,element order
http://jas.shahroodut.ac.ir/article_727.html
http://jas.shahroodut.ac.ir/article_727_c70536bdd3b43cb9e978c4423102d125.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
4
1
2016
09
01
STRONGLY DUO AND CO-MULTIPLICATION MODULES
53
64
EN
S.
Safaeeyan
Department of Mathematics, University of Yasouj , P.O.Box 75914, Yasouj, IRAN.
safaeeyan@mail.yu.ac.ir
10.22044/jas.2016.728
Let R be a commutative ring. An R-module M is called co-multiplication provided that foreach submodule N of M there exists an ideal I of R such that N = (0 : I). In this paper weshow that co-multiplication modules are a generalization of strongly duo modules. Uniserialmodules of finite length and hence valuation Artinian rings are some distinguished classes ofco-multiplication rings. In addition, if R is a Noetherian ring, then R is a strongly duoring if and only if R is a co-multiplication ring. We also show that J-semisimple strongly duorings are precisely semisimple rings. Moreover, if R is a perfect ring, then uniserial R-modules are co-multiplication of finite length modules. Finally, we showthat Abelian co-multiplication groups are reduced and co-multiplication Z-modules(Abeliangroups)are characterized.
Co-multiplication modules,strongly duo modules,Abelian Groups
http://jas.shahroodut.ac.ir/article_728.html
http://jas.shahroodut.ac.ir/article_728_14be7a662ba6a73829b723a3c29433f9.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
4
1
2016
09
01
SIGNED ROMAN DOMINATION NUMBER AND JOIN OF GRAPHS
65
77
EN
A.
Behtoei
Department of Mathematics, Imam Khomeini International University, P.O.Box
34149-16818, Qazvin, Iran.
a.behtoei@sci.ikiu.ac.ir
E.
Vatandoost
Department of Mathematics, Imam Khomeini International University, P.O.Box
34149-16818, Qazvin, Iran.
e-vatandoost@ikiu.ac.ir
F.
Azizi Rajol Abad
Department of Mathematics, Imam Khomeini International University, P.O.Box
34149-16818, Qazvin, Iran.
10.22044/jas.2016.729
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.
Signed Roman domination,Join,Cycle,Wheel,Friendship
http://jas.shahroodut.ac.ir/article_729.html
http://jas.shahroodut.ac.ir/article_729_e681cf062e236a6c154451d27072c3cb.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
4
1
2016
09
01
ARTINIANNESS OF COMPOSED LOCAL COHOMOLOGY MODULES
79
84
EN
H.
Saremi
Department of Mathematics, Sanandaj Branch, University Islamic Azad University,
Sanandaj, Iran.
hero.saremi@gmail.com
10.22044/jas.2016.730
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 $H_{fb}^j(H_{fa}^{d-1}(N))$ is Artinian for all $jgeq 1$.
Generalized local cohomology,Local cohomology,Artinian modules
http://jas.shahroodut.ac.ir/article_730.html
http://jas.shahroodut.ac.ir/article_730_b73d8831c14ac1772432c3f6a0548594.pdf