Factorization numbers of finite abelian groups
Mohammad
Farrokhi Derakhshandeh Ghouchan
Ferdowsi University of Mashhad
author
text
article
2013
eng
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.
International Journal of Group Theory
University of Isfahan
2251-7650
2
v.
2
no.
2013
1
8
http://ijgt.ui.ac.ir/article_1599_d60a3f52cceb029f5491bdf3a82f9f20.pdf
dx.doi.org/10.22108/ijgt.2013.1599
Character expansiveness in finite groups
Zoltan
Halasi
University of Debrecen
author
Attila
Maroti
Renyi Institute of Mathematics
author
Franciska
Petenyi
Technical University of Budapest
author
text
article
2013
eng
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.
International Journal of Group Theory
University of Isfahan
2251-7650
2
v.
2
no.
2013
9
17
http://ijgt.ui.ac.ir/article_1660_4335a14289e50a35e7186085ea9a408c.pdf
dx.doi.org/10.22108/ijgt.2013.1660
On the number of the irreducible characters of factor groups
Amin
Saeidi
Tarbiat Moallem University
author
text
article
2013
eng
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.
International Journal of Group Theory
University of Isfahan
2251-7650
2
v.
2
no.
2013
19
24
http://ijgt.ui.ac.ir/article_1825_6001fd72971d120567ffe1fb9aabb3b8.pdf
dx.doi.org/10.22108/ijgt.2013.1825
On some subgroups associated with the tensor square of a group
Mohammad Mehdi
Nasrabadi
Department of Maths,birjand university
author
Ali
Gholamian
Department of math, birjand university
author
Mohammad Javad
Sadeghifard
Islamic Azad University, Neyshabur branch
author
text
article
2013
eng
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 $[x,g,y]\otimes g=1_{\otimes}$.
International Journal of Group Theory
University of Isfahan
2251-7650
2
v.
2
no.
2013
25
33
http://ijgt.ui.ac.ir/article_1897_1f5905dcbdef0eadf29d39b9305e74be.pdf
dx.doi.org/10.22108/ijgt.2013.1897
Characterization of $A_5$ and $PSL(2,7)$ by sum of element orders
Seyyed Majid
Jafarian Amiri
Department of Mathematics, Faculty of Sciences, University of Zanjan
author
text
article
2013
eng
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 $PSL(2,7)$.
International Journal of Group Theory
University of Isfahan
2251-7650
2
v.
2
no.
2013
35
39
http://ijgt.ui.ac.ir/article_1918_b2e767f38421bf016428f8625e625431.pdf
dx.doi.org/10.22108/ijgt.2013.1918
Certain finite abelian groups with the Redei $k$-property
Sandor
Szabo
Institute of mathematics and Informatics University of Pecs
author
text
article
2013
eng
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 $k$.
International Journal of Group Theory
University of Isfahan
2251-7650
2
v.
2
no.
2013
41
45
http://ijgt.ui.ac.ir/article_1919_137a7158945f7756cc216786d2d47ed9.pdf
dx.doi.org/10.22108/ijgt.2013.1919
Characterization of the symmetric group by its non-commuting graph
Mohammad Reza
Darafsheh
University of Tehran
author
Pedram
Yousefzadeh
K. N. Toosi University of Technology
author
text
article
2013
eng
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.
International Journal of Group Theory
University of Isfahan
2251-7650
2
v.
2
no.
2013
47
72
http://ijgt.ui.ac.ir/article_1920_4d6dd70c53a2f3584898f92c49fe8cf5.pdf
dx.doi.org/10.22108/ijgt.2013.1920