University of IsfahanInternational Journal of Group Theory2251-76502220130601Factorization numbers of finite abelian groups18159910.22108/ijgt.2013.1599ENMohammadFarrokhi Derakhshandeh GhouchanFerdowsi University of MashhadJournal Article20120225The number of factorizations of a finite abelian group as the product of two subgroups is computed in two different ways and a combinatorial identity involving Gaussian binomial coefficients is presented.https://ijgt.ui.ac.ir/article_1599_d60a3f52cceb029f5491bdf3a82f9f20.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76502220130601Character expansiveness in finite groups917166010.22108/ijgt.2013.1660ENZoltanHalasiUniversity of DebrecenAttilaMarotiRenyi Institute of MathematicsFranciskaPetenyiTechnical University of BudapestJournal Article20120606We say that a finite group $G$ is conjugacy expansive if for any normal subset $S$ and any conjugacy class $C$ of $G$ the normal set $SC$ consists of at least as many conjugacy classes of $G$ as $S$ does. Halasi, Mar\'oti, Sidki, Bezerra have shown that a group is conjugacy expansive if and only if it is a direct product of conjugacy expansive simple or abelian groups. By considering a character analogue of the above, we say that a finite group $G$ is character expansive if for any complex character $\alpha$ and irreducible character $\chi$ of $G$ the character $\alpha \chi$ has at least as many irreducible constituents, counting without multiplicity, as $\alpha$ does. In this paper we take some initial steps in determining character expansive groups.https://ijgt.ui.ac.ir/article_1660_4335a14289e50a35e7186085ea9a408c.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76502220130601On the number of the irreducible characters of factor groups1924182510.22108/ijgt.2013.1825ENAminSaeidiTarbiat Moallem UniversityJournal Article20120604Let $G$ be a finite group and let $N$ be a normal subgroup of $G$. Suppose that ${\rm{Irr}} (G | N)$ is the set of the irreducible characters of $G$ that contain $N$ in their kernels. In this paper, we classify solvable groups $G$ in which the set $\mathcal{C} (G) = \{{\rm{Irr}} (G | N) | 1 \ne N \trianglelefteq G \}$ has at most three elements. We also compute the set $\mathcal{C}(G)$ for such groups.https://ijgt.ui.ac.ir/article_1825_6001fd72971d120567ffe1fb9aabb3b8.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76502220130601On some subgroups associated with the tensor square of a group2533189710.22108/ijgt.2013.1897ENMohammad MehdiNasrabadiDepartment of Maths,birjand universityAliGholamianDepartment of math, birjand universityMohammad JavadSadeghifardIslamic Azad University, Neyshabur branchJournal Article20120507In this paper we present some results about subgroup which is generalization of the subgroup $R_{2}^{\otimes}(G)=\{a\in G|[a,g]\otimes g=1_{\otimes},\forall g\in G\}$ of right $2_{\otimes}$-Engel elements of a given group $G$. If $p$ is an odd prime, then with the help of these results, we obtain some results about tensor squares of p-groups satisfying the law $[x,g,y]\otimes g=1_{\otimes}$, for all $x, g, y\in G$. In particular p-groups satisfying the law $[x,g,y]\otimes g=1_{\otimes}$ have abelian tensor squares. Moreover, we can determine tensor squares of two-generator p-groups of class three satisfying the law $[x,g,y]\otimes g=1_{\otimes}$.https://ijgt.ui.ac.ir/article_1897_1f5905dcbdef0eadf29d39b9305e74be.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76502220130601Characterization of A5 and PSL(2, 7) by sum of element orders3539191810.22108/ijgt.2013.1918ENSeyyed MajidJafarian AmiriDepartment of Mathematics, Faculty of Sciences, University of ZanjanJournal Article20120513Let $G$ be a finite group. We denote by $\psi(G)$ the integer $\sum_{g\in G}o(g)$, where $o(g)$ denotes the order of $g \in G$. Here we show that $\psi(A_5)< \psi(G)$ for every non-simple group $G$ of order $60$, where $A_5$ is the alternating group of degree $5$. Also we prove that $\psi(PSL(2,7))<\psi(G)$ for all non-simple groups $G$ of order $168$. These two results confirm the conjecture posed in [J. Algebra Appl., {\bf 10} No. 2 (2011) 187-190] for simple groups $A_5$ and $PSL(2,7)$.https://ijgt.ui.ac.ir/article_1918_b2e767f38421bf016428f8625e625431.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76502220130601Certain finite abelian groups with the Redei $k$-property4145191910.22108/ijgt.2013.1919ENSandorSzaboInstitute of mathematics and Informatics University of PecsJournal Article20120713Three infinite families of finite abelian groups will be described such that each member of these families has the R\'edei $k$-property for many non-trivial values of $k$.https://ijgt.ui.ac.ir/article_1919_137a7158945f7756cc216786d2d47ed9.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76502220130601Characterization of the symmetric group by its non-commuting graph4772192010.22108/ijgt.2013.1920ENMohammad RezaDarafshehUniversity of TehranPedramYousefzadehK. N. Toosi University of TechnologyJournal Article20120830The non-commuting graph $\nabla(G)$ of a non-abelian group $G$ is defined as follows: its vertex set is $G-Z(G)$ and two distinct vertices $x$ and $y$ are joined by an edge if and only if the commutator of $x$ and $y$ is not the identity. In this paper we prove that if $G$ is a finite group with $\nabla(G) \cong \nabla(BS_n)$, then $G \cong BS_n$, where $BS_n$ is the symmetric group of degree $n$, where $n$ is a natural number.https://ijgt.ui.ac.ir/article_1920_4d6dd70c53a2f3584898f92c49fe8cf5.pdf