eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2016-09-01
4
1
1
13
10.22044/jas.2016.724
724
ON RELATIVE CENTRAL EXTENSIONS AND COVERING PAIRS
A. Pourmirzaei
a.pmirzaei@gmail.com
1
M. Hassanzadeh
mtr.hassanzadeh@gmail.com
2
B. Mashayekhy
bmashayekhyf@yahoo.com
3
Department of Mathematics, Hakim Sabzevari University, P. O. Box 96179-76487, Sabzevar, Iran
Department of Mathematics, Department of Mathematics, Ferdowsi University of Mashhad, P.O.Box 1159-91775, Mashhad, Iran.
Department of Mathematics, Center of Excellence in Analysis on Algebraic Struc- tures, Ferdowsi University of Mashhad, P.O.Box 1159-91775, Mashhad, Iran.
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.
http://jas.shahroodut.ac.ir/article_724_70e8def60b0539607f4789672c9b8d32.pdf
Pair of groups
Covering pair
Relative central extension
Isoclinism of pairs of groups
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2016-09-01
4
1
15
27
10.22044/jas.2016.725
725
SOME REMARKS ON GENERALIZATIONS OF MULTIPLICATIVELY CLOSED SUBSETS
M. Ebrahimpour
m.ebrahimpour@vru.ac.ir
1
Department of Mathematics, Faculty of Sciences, Vali-e-Asr University of Rafsanjan , P.O.Box 518, Rafsanjan, Iran
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.
http://jas.shahroodut.ac.ir/article_725_cb149f0b8733858d64345565c0ffefb6.pdf
Multiplication module
Multiplicatively closed subset of R
(n
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2016-09-01
4
1
29
36
10.22044/jas.2016.726
726
ON FINITE GROUPS IN WHICH SS-SEMIPERMUTABILITY IS A TRANSITIVE RELATION
S.E. Mirdamadi
ebrahimmirdamadi@stu.sku.ac.ir
1
Gh.R Rezaeezadeh
gh.rezaeezadeh@yahoo.com
2
Department of Mathematics, University of Shahrekord, P.O.Box 115, Shahrekord, Iran.
Department of Mathematics, University of Shahrekord, P.O.Box 115, Shahrekord, Iran.
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).
http://jas.shahroodut.ac.ir/article_726_4dada44a60bbc33404cb7f7dcf783e40.pdf
SS-semipermutable subgroups
S-semipermutable subgroups
PST-groups
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2016-09-01
4
1
37
51
10.22044/jas.2016.727
727
ON COMPOSITION FACTORS OF A GROUP WITH THE SAME PRIME GRAPH AS Ln(5)
A. Mahmoudifar
alimahmoudifar@gmail.com
1
Department of Mathematics, Tehran North Branch, Islamic Azad University, Tehran, IRAN.
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 $L_n(5)$.
http://jas.shahroodut.ac.ir/article_727_c70536bdd3b43cb9e978c4423102d125.pdf
projective special linear group
prime graph
element order
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2016-09-01
4
1
53
64
10.22044/jas.2016.728
728
STRONGLY DUO AND CO-MULTIPLICATION MODULES
S. Safaeeyan
safaeeyan@mail.yu.ac.ir
1
Department of Mathematics, University of Yasouj , P.O.Box 75914, Yasouj, IRAN.
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.
http://jas.shahroodut.ac.ir/article_728_14be7a662ba6a73829b723a3c29433f9.pdf
Co-multiplication modules
strongly duo modules
Abelian Groups
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2016-09-01
4
1
65
77
10.22044/jas.2016.729
729
SIGNED ROMAN DOMINATION NUMBER AND JOIN OF GRAPHS
A. Behtoei
a.behtoei@sci.ikiu.ac.ir
1
E. Vatandoost
e-vatandoost@ikiu.ac.ir
2
F. Azizi Rajol Abad
3
Department of Mathematics, Imam Khomeini International University, P.O.Box 34149-16818, Qazvin, Iran.
Department of Mathematics, Imam Khomeini International University, P.O.Box 34149-16818, Qazvin, Iran.
Department of Mathematics, Imam Khomeini International University, P.O.Box 34149-16818, Qazvin, Iran.
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.
http://jas.shahroodut.ac.ir/article_729_e681cf062e236a6c154451d27072c3cb.pdf
Signed Roman domination
Join
Cycle
Wheel
Friendship
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2016-09-01
4
1
79
84
10.22044/jas.2016.730
730
ARTINIANNESS OF COMPOSED LOCAL COHOMOLOGY MODULES
H. Saremi
hero.saremi@gmail.com
1
Department of Mathematics, Sanandaj Branch, University Islamic Azad University, Sanandaj, Iran.
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 $jgeq 1$.
http://jas.shahroodut.ac.ir/article_730_b73d8831c14ac1772432c3f6a0548594.pdf
Generalized local cohomology
Local cohomology
Artinian modules