@Article{FarrokhiDerakhshandehGhouchan2013,
author="Farrokhi Derakhshandeh Ghouchan, Mohammad",
title="Factorization numbers of finite abelian groups",
journal="International Journal of Group Theory",
year="2013",
volume="2",
number="2",
pages="1-8",
abstract="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.",
issn="2251-7650",
doi="10.22108/ijgt.2013.1599",
url="http://ijgt.ui.ac.ir/article_1599.html"
}
@Article{Halasi2013,
author="Halasi, Zoltan
and Maroti, Attila
and Petenyi, Franciska",
title="Character expansiveness in finite groups",
journal="International Journal of Group Theory",
year="2013",
volume="2",
number="2",
pages="9-17",
abstract="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.",
issn="2251-7650",
doi="10.22108/ijgt.2013.1660",
url="http://ijgt.ui.ac.ir/article_1660.html"
}
@Article{Saeidi2013,
author="Saeidi, Amin",
title="On the number of the irreducible characters of factor groups",
journal="International Journal of Group Theory",
year="2013",
volume="2",
number="2",
pages="19-24",
abstract="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.",
issn="2251-7650",
doi="10.22108/ijgt.2013.1825",
url="http://ijgt.ui.ac.ir/article_1825.html"
}
@Article{Nasrabadi2013,
author="Nasrabadi, Mohammad Mehdi
and Gholamian, Ali
and Sadeghifard, Mohammad Javad",
title="On some subgroups associated with the tensor square of a group",
journal="International Journal of Group Theory",
year="2013",
volume="2",
number="2",
pages="25-33",
abstract="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 $[x,g,y]\otimes g=1_{\otimes}$.",
issn="2251-7650",
doi="10.22108/ijgt.2013.1897",
url="http://ijgt.ui.ac.ir/article_1897.html"
}
@Article{JafarianAmiri2013,
author="Jafarian Amiri, Seyyed Majid",
title="Characterization of $A_5$ and $PSL(2,7)$ by sum of element orders",
journal="International Journal of Group Theory",
year="2013",
volume="2",
number="2",
pages="35-39",
abstract="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 $PSL(2,7)$.",
issn="2251-7650",
doi="10.22108/ijgt.2013.1918",
url="http://ijgt.ui.ac.ir/article_1918.html"
}
@Article{Szabo2013,
author="Szabo, Sandor",
title="Certain finite abelian groups with the Redei $k$-property",
journal="International Journal of Group Theory",
year="2013",
volume="2",
number="2",
pages="41-45",
abstract="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 $k$.",
issn="2251-7650",
doi="10.22108/ijgt.2013.1919",
url="http://ijgt.ui.ac.ir/article_1919.html"
}
@Article{Darafsheh2013,
author="Darafsheh, Mohammad Reza
and Yousefzadeh, Pedram",
title="Characterization of the symmetric group by its non-commuting graph",
journal="International Journal of Group Theory",
year="2013",
volume="2",
number="2",
pages="47-72",
abstract="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.",
issn="2251-7650",
doi="10.22108/ijgt.2013.1920",
url="http://ijgt.ui.ac.ir/article_1920.html"
}