University of Isfahan International Journal of Group Theory 2251-7650 1 3 2012 09 01 On Huppert's conjecture for F4(2) 1 9 763 10.22108/ijgt.2012.763 EN Hung P Tong-Viet North-West University, Mafikeng Campus Thomas P Wakefield Youngstown State University Journal Article 2011 11 24 Let $G$ be a finite group and let $\text{cd}(G)$ be the set of all‎ ‎complex irreducible character degrees of $G$‎. ‎B‎. ‎Huppert conjectured‎ ‎that if $H$ is a finite nonabelian simple group such that‎ ‎$\text{cd}(G) =\text{cd}(H)$‎, ‎then $G\cong H \times A$‎, ‎where $A$ is‎ ‎an abelian group‎. ‎In this paper‎, ‎we verify the conjecture for‎ ‎${F_4(2)}.$‎ https://ijgt.ui.ac.ir/article_763_84125d4a5e2e7ac9630a1081299e34f0.pdf
University of Isfahan International Journal of Group Theory 2251-7650 1 3 2012 09 01 On finite A-perfect abelian groups 11 14 764 10.22108/ijgt.2012.764 EN Mohammad Mehdi Nasrabadi Department of Maths,birjand university Ali Gholamian Department of mathematics, Birjand university, Birjand Journal Article 2011 11 17 ‎Let $G$ be a group and $A=Aut(G)$ be the group of automorphisms of‎ ‎$G$‎. ‎Then the element $[g,\alpha]=g^{-1}\alpha(g)$ is an‎ ‎autocommutator of $g\in G$ and $\alpha\in A$‎. ‎Also‎, ‎the‎ ‎autocommutator subgroup of G is defined to be‎ ‎$K(G)=\langle[g,\alpha]|g\in G‎, ‎\alpha\in A\rangle$‎, ‎which is a‎ ‎characteristic subgroup of $G$ containing the derived subgroup‎ ‎$G'$ of $G$‎. ‎A group is defined as A-perfect‎, ‎if it equals its own‎ ‎autocommutator subgroup‎. ‎The present research is aimed at‎ ‎classifying finite abelian groups which are A-perfect‎. https://ijgt.ui.ac.ir/article_764_c0e46ef10fc8cc8252147940e51d0023.pdf
University of Isfahan International Journal of Group Theory 2251-7650 1 3 2012 09 01 A new characterization of PSL(2, 25) 15 19 765 10.22108/ijgt.2012.765 EN Alireza Khalili Asboei Babol Education, Mazandaran, Iran Syyed Sadegh Salehi Amiri Islamic Azad University Babol Branch Journal Article 2012 01 15 ‎Let $G$ be a finite group and $\pi_{e}(G)$ be the set of element‎ ‎orders of $G$‎. ‎Let $k \in \pi_{e}(G)$ and $m_{k}$ be the number of‎ ‎elements of order $k$ in $G$‎. ‎Set nse($G$):=$\{ m_{k} | k \in‎ ‎\pi_{e}(G)\}$‎. ‎In this paper‎, ‎we prove that if $G$ is a group such‎ ‎that nse($G$)=nse($PSL(2‎, ‎25)$)‎, ‎then $G \cong PSL(2‎, ‎25)$‎. https://ijgt.ui.ac.ir/article_765_3cb589fd74c1a6fe0587c1d1dc0a64f1.pdf
University of Isfahan International Journal of Group Theory 2251-7650 1 3 2012 09 01 On the semi cover-avoiding property and $\mathcal{F}$-supplementation 21 31 996 10.22108/ijgt.2012.996 EN Changwen Li xuzhou normal university Xiaolan Yi Journal Article 2012 01 14 In this paper‎, ‎we investigate the influence of some subgroups of Sylow subgroups with semi cover-avoiding property and‎ ‎$\mathcal{F}$-supplementation on the structure of finite groups and generalize a series of known results‎. https://ijgt.ui.ac.ir/article_996_fb53e9a8f41d8c6c5704d4c48beabbc2.pdf
University of Isfahan International Journal of Group Theory 2251-7650 1 3 2012 09 01 On varietal capability of Infinite direct products of groups 33 37 850 10.22108/ijgt.2012.850 EN Hanieh Mirebrahimi Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, P. O. Box 1159-91775, Mashhad, Iran Behrooz Mashayekhy Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, P. O. Box 1159-91775, Mashhad, Iran Journal Article 2012 05 07 Recently‎, ‎the authors gave some conditions under which a direct product‎ ‎of finitely many groups is $\mathcal{V}-$capable if and only if each of its‎ ‎factors is $\mathcal{V}-$capable for some varieties $\mathcal{V}$‎. ‎In this paper‎, ‎we extend this fact to any infinite direct product of groups‎. ‎Moreover‎, ‎we conclude some results for $\mathcal{V}-$capability of direct products of infinitely many groups in varieties of abelian‎, ‎nilpotent and polynilpotent groups‎. https://ijgt.ui.ac.ir/article_850_c7158d00eaa639c32430a262f09c81fa.pdf
University of Isfahan International Journal of Group Theory 2251-7650 1 3 2012 09 01 Infinite groups with many generalized normal subgroups 39 49 1223 10.22108/ijgt.2012.1223 EN Francesco De Giovanni Dipartimento di Matematica e Applicazioni - University of Napoli Federico II Caterina Rainone Universita di Napoli Federico II Journal Article 2012 03 21 A subgroup $X$ of a group $G$ is almost normal if the index $|G:N_G(X)|$ is finite‎, ‎while $X$ is nearly normal if it has finite index in the normal closure $X^G$‎. ‎This paper investigates the structure of groups in which every (infinite) subgroup is either almost normal or nearly normal‎. https://ijgt.ui.ac.ir/article_1223_150426f6f6fcaf626f8a811ef1dd2718.pdf
University of Isfahan International Journal of Group Theory 2251-7650 1 3 2012 09 01 Quasirecognition by prime graph of U3(q) where 2 < q = pα < 100 51 66 1369 10.22108/ijgt.2012.1369 EN Seyed Sadegh Salehi Amiri Islamic Azad University Alireza Khalili Asboei Islamic Azad University Ali Iranmanesh Tarbiat Modares University Abolfazl Tehranian Islamic Azad University Journal Article 2012 03 09 Let $G$ be a finite group and let $\Gamma(G)$ be the prime graph‎ ‎of G‎. ‎Assume $2 < q = p^{\alpha} < 100$‎. ‎We determine finite groups‎ ‎G such that $\Gamma(G) = \Gamma(U_3(q))$ and prove that if $q \neq‎ ‎3‎, ‎5‎, ‎9‎, ‎17$‎, ‎then $U_3(q)$ is quasirecognizable by prime graph‎, ‎i.e‎. ‎if $G$ is a finite group with the same prime graph as the‎ ‎finite simple group $U_3(q)$‎, ‎then $G$ has a unique non-Abelian‎ ‎composition factor isomorphic to $U_3(q)$‎. ‎As a consequence of our‎ ‎results‎, ‎we prove that the simple groups $U_{3}(8)$ and $U_{3}(11)$‎ ‎are $4-$recognizable and $2-$recognizable by prime graph‎, ‎respectively‎. ‎In fact‎, ‎the group $U_{3}(8)$ is the first example‎ ‎which is a $4-$recognizable by prime graph‎. https://ijgt.ui.ac.ir/article_1369_3a2c5d4f00b6ca4392b6fc4dafbcde67.pdf