@Article{Ebrahimzadeh2017,
author="Ebrahimzadeh, Behnam
and Iranmanesh, Ali
and Parvizi Mosaed, Hosein",
title="A new characterization of Ree group $\mathbf{{}^2G_2(q)}$ by the order of group and the number of elements with the same order",
journal="International Journal of Group Theory",
year="2017",
volume="6",
number="4",
pages="1-6",
abstract="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.",
issn="2251-7650",
doi="10.22108/ijgt.2017.21233",
url="http://ijgt.ui.ac.ir/article_21233.html"
}
@Article{Staroletov2017,
author="Staroletov, Alexey",
title="On almost recognizability by spectrum of simple classical groups",
journal="International Journal of Group Theory",
year="2017",
volume="6",
number="4",
pages="7-33",
abstract="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.",
issn="2251-7650",
doi="10.22108/ijgt.2017.21223",
url="http://ijgt.ui.ac.ir/article_21223.html"
}
@Article{Mousavi2017,
author="Mousavi, Hamid
and Rezazadeh, Zahra",
title="Finite non-nilpotent groups with few non-normal non-cyclic subgroups",
journal="International Journal of Group Theory",
year="2017",
volume="6",
number="4",
pages="35-40",
abstract="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.",
issn="2251-7650",
doi="10.22108/ijgt.2017.21222",
url="http://ijgt.ui.ac.ir/article_21222.html"
}
@Article{Hafezieh2017,
author="Hafezieh, Roghayeh",
title="Bipartite divisor graph for the set of irreducible character degrees",
journal="International Journal of Group Theory",
year="2017",
volume="6",
number="4",
pages="41-51",
abstract="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.",
issn="2251-7650",
doi="10.22108/ijgt.2017.21221",
url="http://ijgt.ui.ac.ir/article_21221.html"
}
@Article{Mpono2017,
author="Mpono, Zwelethemba",
title="The conjugacy class ranks of $M_{24}$",
journal="International Journal of Group Theory",
year="2017",
volume="6",
number="4",
pages="53-58",
abstract="$M_{24}$ 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.",
issn="2251-7650",
doi="10.22108/ijgt.2017.21477",
url="http://ijgt.ui.ac.ir/article_21477.html"
}