ORIGINAL_ARTICLE Factorization numbers of finite abelian groups The 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. http://ijgt.ui.ac.ir/article_1599_d60a3f52cceb029f5491bdf3a82f9f20.pdf 2013-06-01T11:23:20 2019-05-24T11:23:20 1 8 10.22108/ijgt.2013.1599 Factorization number‎ ‎Abelian group‎ ‎subgroup‎ ‎Gaussian‎ ‎binomial coefficient Mohammad Farrokhi Derakhshandeh Ghouchan 14999825@mmm.muroran-it.ac.jp true 1 Ferdowsi University of Mashhad Ferdowsi University of Mashhad Ferdowsi University of Mashhad LEAD_AUTHOR
ORIGINAL_ARTICLE Character expansiveness in finite groups We 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. http://ijgt.ui.ac.ir/article_1660_4335a14289e50a35e7186085ea9a408c.pdf 2013-06-01T11:23:20 2019-05-24T11:23:20 9 17 10.22108/ijgt.2013.1660 Finite group Irreducible characters product of characters Zoltan Halasi halasi.zoltan@reny.mta.hu true 1 University of Debrecen University of Debrecen University of Debrecen AUTHOR Attila Maroti maroti.attila@renyi.mta.hu true 2 Renyi Institute of Mathematics Renyi Institute of Mathematics Renyi Institute of Mathematics LEAD_AUTHOR Franciska Petenyi petenyi.franciska@gmail.com true 3 Technical University of Budapest Technical University of Budapest Technical University of Budapest AUTHOR
ORIGINAL_ARTICLE On the number of the irreducible characters of factor groups ‎Let $G$ 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. http://ijgt.ui.ac.ir/article_1825_6001fd72971d120567ffe1fb9aabb3b8.pdf 2013-06-01T11:23:20 2019-05-24T11:23:20 19 24 10.22108/ijgt.2013.1825 Irreducible characters Conjugacy classes minimal normal subgroups Frobenius groups Amin Saeidi saeidi.amin@gmail.com true 1 Tarbiat Moallem University Tarbiat Moallem University Tarbiat Moallem University LEAD_AUTHOR
ORIGINAL_ARTICLE On some subgroups associated with the tensor square of a group ‎In 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 $[x,g,y]\otimes g=1_{\otimes}$‎. http://ijgt.ui.ac.ir/article_1897_1f5905dcbdef0eadf29d39b9305e74be.pdf 2013-06-01T11:23:20 2019-05-24T11:23:20 25 33 10.22108/ijgt.2013.1897 Non-abelian tensor square Engel elements of a group p-groups Mohammad Mehdi Nasrabadi nasrabadimm@yahoo.com true 1 Department of Maths,birjand university Department of Maths,birjand university Department of Maths,birjand university LEAD_AUTHOR Ali Gholamian ali.ghfath@gmail.com true 2 Department of math, birjand university Department of math, birjand university Department of math, birjand university AUTHOR Mohammad Javad Sadeghifard math.sadeghifard85@gmail.com true 3 Islamic Azad University, Neyshabur branch Islamic Azad University, Neyshabur branch Islamic Azad University, Neyshabur branch AUTHOR
ORIGINAL_ARTICLE Characterization of‎ ‎$A_5$ and $PSL(2,7)$ by sum of element orders Let $G$ 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 $PSL(2,7)$‎. http://ijgt.ui.ac.ir/article_1918_b2e767f38421bf016428f8625e625431.pdf 2013-06-01T11:23:20 2019-05-24T11:23:20 35 39 10.22108/ijgt.2013.1918 Finite groups simple group element orders Seyyed Majid Jafarian Amiri sm_jafarian@znu.ac.ir true 1 Department of Mathematics, Faculty of Sciences, University of Zanjan Department of Mathematics, Faculty of Sciences, University of Zanjan Department of Mathematics, Faculty of Sciences, University of Zanjan LEAD_AUTHOR
ORIGINAL_ARTICLE Certain finite abelian groups with the Redei $k$-property ‎Three 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 $k$‎. http://ijgt.ui.ac.ir/article_1919_137a7158945f7756cc216786d2d47ed9.pdf 2013-06-01T11:23:20 2019-05-24T11:23:20 41 45 10.22108/ijgt.2013.1919 Factoring abelian groups periodic subsets full-rank subsets Hajos $k$-property Redei $k$-property Sandor Szabo sszabo7@hotmail.com true 1 Institute of mathematics and Informatics University of Pecs Institute of mathematics and Informatics University of Pecs Institute of mathematics and Informatics University of Pecs LEAD_AUTHOR
ORIGINAL_ARTICLE Characterization of the symmetric group by its non-commuting graph ‎The 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. http://ijgt.ui.ac.ir/article_1920_4d6dd70c53a2f3584898f92c49fe8cf5.pdf 2013-06-01T11:23:20 2019-05-24T11:23:20 47 72 10.22108/ijgt.2013.1920 Keywords and phrases: non-commuting graph symmetric group Finite groups Mohammad Reza Darafsheh darafsheh@ut.ac.ir true 1 University of Tehran University of Tehran University of Tehran AUTHOR Pedram Yousefzadeh pedram_yous@yahoo.com true 2 K. N. Toosi University of Technology K. N. Toosi University of Technology K. N. Toosi University of Technology LEAD_AUTHOR