University of Isfahan International Journal of Group Theory 2251-7650 2 2 2013 06 01 Factorization numbers of finite abelian groups 1 8 1599 10.22108/ijgt.2013.1599 EN Mohammad Farrokhi Derakhshandeh Ghouchan Ferdowsi University of Mashhad Journal Article 2012 02 25 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. https://ijgt.ui.ac.ir/article_1599_d60a3f52cceb029f5491bdf3a82f9f20.pdf
University of Isfahan International Journal of Group Theory 2251-7650 2 2 2013 06 01 Character expansiveness in finite groups 9 17 1660 10.22108/ijgt.2013.1660 EN Zoltan Halasi University of Debrecen Attila Maroti Renyi Institute of Mathematics Franciska Petenyi Technical University of Budapest Journal Article 2012 06 06 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. https://ijgt.ui.ac.ir/article_1660_4335a14289e50a35e7186085ea9a408c.pdf
University of Isfahan International Journal of Group Theory 2251-7650 2 2 2013 06 01 On the number of the irreducible characters of factor groups 19 24 1825 10.22108/ijgt.2013.1825 EN Amin Saeidi Tarbiat Moallem University Journal Article 2012 06 04 ‎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. https://ijgt.ui.ac.ir/article_1825_6001fd72971d120567ffe1fb9aabb3b8.pdf
University of Isfahan International Journal of Group Theory 2251-7650 2 2 2013 06 01 On some subgroups associated with the tensor square of a group 25 33 1897 10.22108/ijgt.2013.1897 EN Mohammad Mehdi Nasrabadi Department of Maths,birjand university Ali Gholamian Department of math, birjand university Mohammad Javad Sadeghifard Islamic Azad University, Neyshabur branch Journal Article 2012 05 07 ‎In this paper we present some results about subgroup which is‎ ‎generalization of the subgroup \$R_{2}^{otimes}(G)={ain‎ ‎G|[a,g]otimes g=1_{otimes},forall gin 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, ‎yin 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.pdf
University of Isfahan International Journal of Group Theory 2251-7650 2 2 2013 06 01 Characterization of‎ ‎\$A_5\$ and \$PSL(2,7)\$ by sum of element orders 35 39 1918 10.22108/ijgt.2013.1918 EN Seyyed Majid Jafarian Amiri Department of Mathematics, Faculty of Sciences, University of Zanjan Journal Article 2012 05 13 Let \$G\$ be a finite group‎. ‎We denote by \$psi(G)\$ the integer \$sum_{gin 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.pdf
University of Isfahan International Journal of Group Theory 2251-7650 2 2 2013 06 01 Certain finite abelian groups with the Redei \$k\$-property 41 45 1919 10.22108/ijgt.2013.1919 EN Sandor Szabo Institute of mathematics and Informatics University of Pecs Journal Article 2012 07 13 ‎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\$‎. https://ijgt.ui.ac.ir/article_1919_137a7158945f7756cc216786d2d47ed9.pdf
University of Isfahan International Journal of Group Theory 2251-7650 2 2 2013 06 01 Characterization of the symmetric group by its non-commuting graph 47 72 1920 10.22108/ijgt.2013.1920 EN Mohammad Reza Darafsheh University of Tehran Pedram Yousefzadeh K. N. Toosi University of Technology Journal Article 2012 08 30 ‎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. https://ijgt.ui.ac.ir/article_1920_4d6dd70c53a2f3584898f92c49fe8cf5.pdf