University of Isfahan International Journal of Group Theory 2251-7650 2251-7669 2 2 2013 06 01 Factorization numbers of finite abelian groups 1 8 EN Mohammad Farrokhi Derakhshandeh Ghouchan Ferdowsi University of Mashhad 14999825@mmm.muroran-it.ac.jp 10.22108/ijgt.2013.1599 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. Factorization number‎,‎Abelian group‎,‎subgroup‎,‎Gaussian‎ ‎binomial coefficient http://ijgt.ui.ac.ir/article_1599.html http://ijgt.ui.ac.ir/article_1599_d60a3f52cceb029f5491bdf3a82f9f20.pdf
University of Isfahan International Journal of Group Theory 2251-7650 2251-7669 2 2 2013 06 01 Character expansiveness in finite groups 9 17 EN Zoltan Halasi University of Debrecen halasi.zoltan@reny.mta.hu Attila Maroti Renyi Institute of Mathematics maroti.attila@renyi.mta.hu Franciska Petenyi Technical University of Budapest petenyi.franciska@gmail.com 10.22108/ijgt.2013.1660 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. Finite group,Irreducible characters,product of characters http://ijgt.ui.ac.ir/article_1660.html http://ijgt.ui.ac.ir/article_1660_4335a14289e50a35e7186085ea9a408c.pdf
University of Isfahan International Journal of Group Theory 2251-7650 2251-7669 2 2 2013 06 01 On the number of the irreducible characters of factor groups 19 24 EN Amin Saeidi Tarbiat Moallem University saeidi.amin@gmail.com 10.22108/ijgt.2013.1825 ‎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. Irreducible characters,Conjugacy classes,minimal normal subgroups,Frobenius groups http://ijgt.ui.ac.ir/article_1825.html http://ijgt.ui.ac.ir/article_1825_6001fd72971d120567ffe1fb9aabb3b8.pdf