eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2013-06-01
2
2
1
8
1599
Factorization numbers of finite abelian groups
Mohammad Farrokhi Derakhshandeh Ghouchan
14999825@mmm.muroran-it.ac.jp
1
Ferdowsi University of Mashhad
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
Factorization number
Abelian group
subgroup
Gaussian binomial coefficient
eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2013-06-01
2
2
9
17
1660
Character expansiveness in finite groups
Zoltan Halasi
halasi.zoltan@reny.mta.hu
1
Attila Maroti
maroti.attila@renyi.mta.hu
2
Franciska Petenyi
petenyi.franciska@gmail.com
3
University of Debrecen
Renyi Institute of Mathematics
Technical University of Budapest
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
Finite group
Irreducible characters
product of
characters
eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2013-06-01
2
2
19
24
1825
On the number of the irreducible characters of factor groups
Amin Saeidi
saeidi.amin@gmail.com
1
Tarbiat Moallem University
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
Irreducible characters
Conjugacy classes
minimal normal subgroups
Frobenius groups
eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2013-06-01
2
2
25
33
1897
On some subgroups associated with the tensor square of a group
Mohammad Mehdi Nasrabadi
nasrabadimm@yahoo.com
1
Ali Gholamian
ali.ghfath@gmail.com
2
Mohammad Javad Sadeghifard
math.sadeghifard85@gmail.com
3
Department of Maths,birjand university
Department of math, birjand university
Islamic Azad University, Neyshabur branch
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 $[x,g,y]otimes g=1_{otimes}$.
http://ijgt.ui.ac.ir/article_1897_1f5905dcbdef0eadf29d39b9305e74be.pdf
Non-abelian tensor square
Engel elements of a group
p-groups
eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2013-06-01
2
2
35
39
1918
Characterization of $A_5$ and $PSL(2,7)$ by sum of element orders
Seyyed Majid Jafarian Amiri
sm_jafarian@znu.ac.ir
1
Department of Mathematics, Faculty of Sciences, University of Zanjan
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))
http://ijgt.ui.ac.ir/article_1918_b2e767f38421bf016428f8625e625431.pdf
finite groups
simple group
element orders
eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2013-06-01
2
2
41
45
1919
Certain finite abelian groups with the Redei $k$-property
Sandor Szabo
sszabo7@hotmail.com
1
Institute of mathematics and Informatics University of Pecs
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
Factoring abelian groups
periodic subsets
full-rank subsets
Hajos $k$-property
Redei $k$-property
eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2013-06-01
2
2
47
72
1920
Characterization of the symmetric group by its non-commuting graph
Mohammad Reza Darafsheh
darafsheh@ut.ac.ir
1
Pedram Yousefzadeh
pedram_yous@yahoo.com
2
University of Tehran
K. N. Toosi University of Technology
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
Keywords and phrases: non-commuting graph
symmetric group
finite groups