University of IsfahanInternational Journal of Group Theory2251-76506420171201A new characterization of ree group2g2 (Q) by the order of group and the number of elements with the same order162123310.22108/ijgt.2017.21233ENBehnamEbrahimzadeh‎Islamic Azad UniversityAliIranmaneshTarbiat Modares UniversityHoseinParvizi MosaedAlvand Institute of Higher EducationJournal Article20151230In 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.https://ijgt.ui.ac.ir/article_21233_8adb8053fff18fb8b8e4f2a357fc36fc.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76506420171201On al most recognizability by spectrum of simple classical groups7332122310.22108/ijgt.2017.21223ENAlexeyStaroletovJournal Article20160711The 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.https://ijgt.ui.ac.ir/article_21223_a27f1a953c35563d61b262716c162d8d.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76506420171201Finite non-nilpotent groups with few non-normal non-cyclic subgroups35402122210.22108/ijgt.2017.21222ENHamidMousaviDepartment of Mathematical Sciences, University of Tabriz, P.O.Box 51666-16471, Tabriz, IranZahraRezazadehDepartment of Mathematical Sciences, Isfahan University of Technology, P.O.Box 84156-83111, Isfahan, IranJournal Article20161102For 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.https://ijgt.ui.ac.ir/article_21222_74ea1917797ce7c347bc70065b3eeeee.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76506420171201Bipartite divisor graph for the set of irreducible character degrees41512122110.22108/ijgt.2017.21221ENRoghayehHafeziehGEBZE TECHNICAL UNIV.Journal Article20160701Let $G$ 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.https://ijgt.ui.ac.ir/article_21221_f95dd0c816b18095ff14239df788d586.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76506420171201The conjugacy class ranks of $M_{24}$53582147710.22108/ijgt.2017.21477ENZwelethembaMponoUniversity of South AfricaJournal Article20160226$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.https://ijgt.ui.ac.ir/article_21477_6cfa78b3346ee6b6396dfb71e724aa80.pdf