ON RELATIVE CENTRAL EXTENSIONS AND COVERING PAIRS
A.
Pourmirzaei
Department of Mathematics, Hakim Sabzevari University, P. O. Box 96179-76487,
Sabzevar, Iran
author
M.
Hassanzadeh
Department of Mathematics, Department of Mathematics, Ferdowsi University of
Mashhad, P.O.Box 1159-91775, Mashhad, Iran.
author
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.
author
text
article
2016
eng
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.
Journal of Algebraic Systems
Shahrood University of Technology
2345-5128
4
v.
1
no.
2016
1
13
http://jas.shahroodut.ac.ir/article_724_70e8def60b0539607f4789672c9b8d32.pdf
dx.doi.org/10.22044/jas.2016.724
SOME REMARKS ON GENERALIZATIONS OF MULTIPLICATIVELY CLOSED SUBSETS
M.
Ebrahimpour
Department of Mathematics, Faculty of Sciences, Vali-e-Asr University of Rafsanjan
, P.O.Box 518, Rafsanjan, Iran
author
text
article
2016
eng
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.
Journal of Algebraic Systems
Shahrood University of Technology
2345-5128
4
v.
1
no.
2016
15
27
http://jas.shahroodut.ac.ir/article_725_cb149f0b8733858d64345565c0ffefb6.pdf
dx.doi.org/10.22044/jas.2016.725
ON FINITE GROUPS IN WHICH SS-SEMIPERMUTABILITY IS A TRANSITIVE RELATION
S.E.
Mirdamadi
Department of Mathematics, University of Shahrekord, P.O.Box 115, Shahrekord,
Iran.
author
Gh.R
Rezaeezadeh
Department of Mathematics, University of Shahrekord, P.O.Box 115, Shahrekord,
Iran.
author
text
article
2016
eng
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).
Journal of Algebraic Systems
Shahrood University of Technology
2345-5128
4
v.
1
no.
2016
29
36
http://jas.shahroodut.ac.ir/article_726_4dada44a60bbc33404cb7f7dcf783e40.pdf
dx.doi.org/10.22044/jas.2016.726
ON COMPOSITION FACTORS OF A GROUP WITH THE SAME PRIME GRAPH AS Ln(5)
A.
Mahmoudifar
Department of Mathematics, Tehran North Branch, Islamic Azad University, Tehran,
IRAN.
author
text
article
2016
eng
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 $L_n(5)$.
Journal of Algebraic Systems
Shahrood University of Technology
2345-5128
4
v.
1
no.
2016
37
51
http://jas.shahroodut.ac.ir/article_727_c70536bdd3b43cb9e978c4423102d125.pdf
dx.doi.org/10.22044/jas.2016.727
STRONGLY DUO AND CO-MULTIPLICATION MODULES
S.
Safaeeyan
Department of Mathematics, University of Yasouj , P.O.Box 75914, Yasouj, IRAN.
author
text
article
2016
eng
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.
Journal of Algebraic Systems
Shahrood University of Technology
2345-5128
4
v.
1
no.
2016
53
64
http://jas.shahroodut.ac.ir/article_728_14be7a662ba6a73829b723a3c29433f9.pdf
dx.doi.org/10.22044/jas.2016.728
SIGNED ROMAN DOMINATION NUMBER AND JOIN OF GRAPHS
A.
Behtoei
Department of Mathematics, Imam Khomeini International University, P.O.Box
34149-16818, Qazvin, Iran.
author
E.
Vatandoost
Department of Mathematics, Imam Khomeini International University, P.O.Box
34149-16818, Qazvin, Iran.
author
F.
Azizi Rajol Abad
Department of Mathematics, Imam Khomeini International University, P.O.Box
34149-16818, Qazvin, Iran.
author
text
article
2016
eng
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.
Journal of Algebraic Systems
Shahrood University of Technology
2345-5128
4
v.
1
no.
2016
65
77
http://jas.shahroodut.ac.ir/article_729_e681cf062e236a6c154451d27072c3cb.pdf
dx.doi.org/10.22044/jas.2016.729
ARTINIANNESS OF COMPOSED LOCAL COHOMOLOGY MODULES
H.
Saremi
Department of Mathematics, Sanandaj Branch, University Islamic Azad University,
Sanandaj, Iran.
author
text
article
2016
eng
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 $jgeq 1$.
Journal of Algebraic Systems
Shahrood University of Technology
2345-5128
4
v.
1
no.
2016
79
84
http://jas.shahroodut.ac.ir/article_730_b73d8831c14ac1772432c3f6a0548594.pdf
dx.doi.org/10.22044/jas.2016.730