A new characterization of Ree group $\mathbf{{}^2G_2(q)}$ by the order of group and the number of elements with the same order
Behnam
Ebrahimzadeh
‎Islamic Azad University
author
Ali
Iranmanesh
Tarbiat Modares University
author
Hosein
Parvizi Mosaed
Alvand Institute of Higher Education
author
text
article
2017
eng
In this paper, we prove that Ree group ${}^2G_2(q)$, where $q\pm\sqrt{3q}+1$ is a prime number can be uniquely determined by the order of group and the number of elements with the same order.
International Journal of Group Theory
University of Isfahan
2251-7650
6
v.
4
no.
2017
1
6
http://ijgt.ui.ac.ir/article_21233_8adb8053fff18fb8b8e4f2a357fc36fc.pdf
dx.doi.org/10.22108/ijgt.2017.21233
On almost recognizability by spectrum of simple classical groups
Alexey
Staroletov
author
text
article
2017
eng
The set of element orders of a finite group $G$ is called the {\em spectrum}. Groups with coinciding spectra are said to be {\em isospectral}. It is known that if $G$ has a nontrivial normal soluble subgroup then there exist infinitely many pairwise non-isomorphic groups isospectral to $G$. The situation is quite different if $G$ is a nonabelain simple group. Recently it was proved that if $L$ is a simple classical group of dimension at least 62 and $G$ is a finite group isospectral to $L$, then up to isomorphism $L\leq G\leq\Aut L$. We show that the assertion remains true if 62 is replaced by 38.
International Journal of Group Theory
University of Isfahan
2251-7650
6
v.
4
no.
2017
7
33
http://ijgt.ui.ac.ir/article_21223_a27f1a953c35563d61b262716c162d8d.pdf
dx.doi.org/10.22108/ijgt.2017.21223
Finite non-nilpotent groups with few non-normal non-cyclic subgroups
Hamid
Mousavi
Department of Mathematical Sciences, University of Tabriz, P.O.Box 51666-16471, Tabriz, Iran
author
Zahra
Rezazadeh
Department of Mathematical Sciences, Isfahan University of Technology, P.O.Box 84156-83111, Isfahan, Iran
author
text
article
2017
eng
For a finite group $G$, let $\nu_{nc}(G)$ denote the number of conjugacy classes of non-normal non-cyclic subgroups of $G$. We characterize the finite non-nilpotent groups whose all non-normal non-cyclic subgroups are conjugate.
International Journal of Group Theory
University of Isfahan
2251-7650
6
v.
4
no.
2017
35
40
http://ijgt.ui.ac.ir/article_21222_74ea1917797ce7c347bc70065b3eeeee.pdf
dx.doi.org/10.22108/ijgt.2017.21222
Bipartite divisor graph for the set of irreducible character degrees
Roghayeh
Hafezieh
GEBZE TECHNICAL UNIV.
author
text
article
2017
eng
Let $G$ be a finite group. We consider the set of the irreducible complex characters of $G$, namely $Irr(G)$, and the related degree set $cd(G)=\{\chi(1) : \chi\in Irr(G)\}$. Let $\rho(G)$ be the set of all primes which divide some character degree of $G$. In this paper we introduce the bipartite divisor graph for $cd(G)$ as an undirected bipartite graph with vertex set $\rho(G)\cup (cd(G)\setminus\{1\})$, such that an element $p$ of $\rho(G)$ is adjacent to an element $m$ of $cd(G)\setminus\{1\}$ if and only if $p$ divides $m$. We denote this graph simply by $B(G)$. Then by means of combinatorial properties of this graph, we discuss the structure of the group $G$. In particular, we consider the cases where $B(G)$ is a path or a cycle.
International Journal of Group Theory
University of Isfahan
2251-7650
6
v.
4
no.
2017
41
51
http://ijgt.ui.ac.ir/article_21221_f95dd0c816b18095ff14239df788d586.pdf
dx.doi.org/10.22108/ijgt.2017.21221
The conjugacy class ranks of $M_{24}$
Zwelethemba
Mpono
University of South Africa
author
text
article
2017
eng
$M_{24}$ is the largest Mathieu sporadic simple group of order $244 823 040 = 2^{10} {\cdot} 3^3 {\cdot} 5 {\cdot} 7 {\cdot} 11 {\cdot} 23$ and contains all the other Mathieu sporadic simple groups as subgroups. The object in this paper is to study the ranks of $M_{24}$ with respect to the conjugacy classes of all its nonidentity elements.
International Journal of Group Theory
University of Isfahan
2251-7650
6
v.
4
no.
2017
53
58
http://ijgt.ui.ac.ir/article_21477_6cfa78b3346ee6b6396dfb71e724aa80.pdf
dx.doi.org/10.22108/ijgt.2017.21477