Shahrood University of TechnologyJournal of Algebraic Systems2345-51284120160901ON RELATIVE CENTRAL EXTENSIONS AND COVERING PAIRS11372410.22044/jas.2016.724ENA. PourmirzaeiDepartment of Mathematics, Hakim Sabzevari University, P. O. Box 96179-76487,
Sabzevar, IranM. HassanzadehDepartment of Mathematics, Department of Mathematics, Ferdowsi University of
Mashhad, P.O.Box 1159-91775, Mashhad, Iran.B. MashayekhyDepartment of Mathematics, Center of Excellence in Analysis on Algebraic Struc-
tures, Ferdowsi University of Mashhad, P.O.Box 1159-91775, Mashhad, Iran.Journal Article20150302Let (G;N) be a pair of groups. In this article, first we con-<br />struct a relative central extension for the pair (G;N) such that special<br />types of covering pair of (G;N) are homomorphic image of it. Second, we<br />show that every perfect pair admits at least one covering pair. Finally,<br />among extending some properties of perfect groups to perfect pairs, we<br />characterize covering pairs of a perfect pair (G;N) under some extra<br />assumptions.Shahrood University of TechnologyJournal of Algebraic Systems2345-51284120160901SOME REMARKS ON GENERALIZATIONS OF MULTIPLICATIVELY CLOSED SUBSETS152772510.22044/jas.2016.725ENM. EbrahimpourDepartment of Mathematics, Faculty of Sciences, Vali-e-Asr University of Rafsanjan
, P.O.Box 518, Rafsanjan, IranJournal Article20150902Let R be a commutative ring with identity and M<br />be a unitary R-module. In this paper we generalize the concept<br />multiplicatively closed subset of R and we study some properties<br />of these genaralized subsets of M. Among the many results in this<br />paper, we generalize some well-known theorems about multiplicatively<br />closed subsets of R to these generalized subsets of M. Also<br />we show that some other well-known results about multiplicatively<br />closed subsets of R are not valid for these generalized subsets of<br />M.Shahrood University of TechnologyJournal of Algebraic Systems2345-51284120160901ON FINITE GROUPS IN WHICH SS-SEMIPERMUTABILITY IS A TRANSITIVE RELATION293672610.22044/jas.2016.726ENS.E. MirdamadiDepartment of Mathematics, University of Shahrekord, P.O.Box 115, Shahrekord,
Iran.Gh.R RezaeezadehDepartment of Mathematics, University of Shahrekord, P.O.Box 115, Shahrekord,
Iran.Journal Article20151021Let H be a subgroup of a finite group G. We say that H is SS-semipermutable in G<br />if H has a supplement K in G such that H permutes with every Sylow subgroup X of K<br />with (jXj; jHj) = 1. In this paper, the Structure of SS-semipermutable subgroups, and finite<br />groups in which SS-semipermutability is a transitive relation are described. It is shown that<br />a finite solvable group G is a PST-group if and only if whenever H K are two p-subgroups<br />of G, H is SS-semipermutable in NG(K).Shahrood University of TechnologyJournal of Algebraic Systems2345-51284120160901ON COMPOSITION FACTORS OF A GROUP WITH THE SAME PRIME GRAPH AS Ln(5)375172710.22044/jas.2016.727ENA. MahmoudifarDepartment of Mathematics, Tehran North Branch, Islamic Azad University, Tehran,
IRAN.Journal Article20151121The prime graph of a finite group $G$ is denoted by<br />$ga(G)$. A nonabelian simple group $G$ is called quasirecognizable by prime<br />graph, if for every finite group $H$, where $ga(H)=ga(G)$, there<br />exists a nonabelian composition factor of $H$ which is isomorphic to<br />$G$. Until now, it is proved that some finite linear simple groups are<br />quasirecognizable 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 the<br />quasirecognition by prime graph of the simple group $L_n(5)$.Shahrood University of TechnologyJournal of Algebraic Systems2345-51284120160901STRONGLY DUO AND CO-MULTIPLICATION MODULES536472810.22044/jas.2016.728ENS. SafaeeyanDepartment of Mathematics, University of Yasouj , P.O.Box 75914, Yasouj, IRAN.Journal Article20151227Let R be a commutative ring. An R-module M is called co-multiplication provided that for<br />each submodule N of M there exists an ideal I of R such that N = (0 : I). In this paper we<br />show that co-multiplication modules are a generalization of strongly duo modules. Uniserial<br />modules of finite length and hence valuation Artinian rings are some distinguished classes of<br />co-multiplication rings. In addition, if R is a Noetherian ring, then R is a strongly duo<br />ring if and only if R is a co-multiplication ring. We also show that J-semisimple strongly duo<br />rings are precisely semisimple rings. Moreover, if R is a perfect ring, then uniserial R-modules are co-multiplication of finite length modules. Finally, we show<br />that Abelian co-multiplication groups are reduced and co-multiplication Z-modules(Abelian<br />groups)are characterized.Shahrood University of TechnologyJournal of Algebraic Systems2345-51284120160901SIGNED ROMAN DOMINATION NUMBER AND JOIN OF GRAPHS657772910.22044/jas.2016.729ENA. BehtoeiDepartment of Mathematics, Imam Khomeini International University, P.O.Box
34149-16818, Qazvin, Iran.E. VatandoostDepartment of Mathematics, Imam Khomeini International University, P.O.Box
34149-16818, Qazvin, Iran.F. Azizi Rajol AbadDepartment of Mathematics, Imam Khomeini International University, P.O.Box
34149-16818, Qazvin, Iran.Journal Article20160221In this paper we study the signed Roman domination<br />number of the join of graphs. Specially, we determine it for the<br />join of cycles, wheels, fans and friendship graphs.Shahrood University of TechnologyJournal of Algebraic Systems2345-51284120160901ARTINIANNESS OF COMPOSED LOCAL COHOMOLOGY MODULES798473010.22044/jas.2016.730ENH. SaremiDepartment of Mathematics, Sanandaj Branch, University Islamic Azad University,
Sanandaj, Iran.Journal Article20160501Let $R$ 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 finitely<br />generated $}$. 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 $jgeq 1$.