University of IsfahanInternational Journal of Group Theory2251-76503220140601Non-nilpotent groups with three conjugacy classes of non-normal subgroups17353310.22108/ijgt.2014.3533ENHamidMousaviDepartment of Mathematics,
University of Tabriz,
P.O.Box 51666-17766,
Tabriz, IranJournal Article20130603For a finite group $G$ let $\nu(G)$ denote the number of conjugacy classes of non-normal subgroups of $G$. The aim of this paper is to classify all the non-nilpotent groups with $\nu(G)=3$.https://ijgt.ui.ac.ir/article_3533_0e6fd95d96bb53d56958d1ad81586935.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76503220140601Second cohomology of Lie rings and the Schur multiplier920358910.22108/ijgt.2014.3589ENMaxHornAG Algebra,
Mathematisches Institut,
Justus-Liebig-Universität Gießen,
Arndtstrasse 2
35392, Giessen, GermanySeiranZandiDepartment of Mathematics, University of Kharazmi,
P.O.Box 15614, Tehran, IranJournal Article20130702We exhibit an explicit construction for the second cohomology group $H^2(L, A)$ for a Lie ring $L$ and a trivial $L$-module $A$. We show how the elements of $H^2(L, A)$ correspond one-to-one to the equivalence classes of central extensions of $L$ by $A$, where $A$ now is considered as an abelian Lie ring. For a finite Lie ring $L$ we also show that $H^2(L, C^*) \cong M(L)$, where $M(L)$ denotes the Schur multiplier of $L$. These results match precisely the analogue situation in group theory.https://ijgt.ui.ac.ir/article_3589_cf135f0fb1340cca48124481e4a34726.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76503220140601The Fischer-Clifford matrices of an extension group of the form 27:(27:S6)2139365910.22108/ijgt.2014.3659ENAbraham LovePrinsStellenbosch UniversityRichard LlewellynFrayUniversity
of the Western CapeJournal Article20130520The split extension group $A(4)\cong 2^7{:}Sp_6(2)$ is the affine subgroup of the symplectic group $Sp_8(2)$ of index $255$. In this paper, we use the technique of the Fischer-Clifford matrices to construct the character table of the inertia group $2^7{:}(2^5{:}S_{6})$ of $A(4)$ of index $63$.https://ijgt.ui.ac.ir/article_3659_db2229030defd2c35f47cd2cd8fb7539.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76503220140601Group actions related to non-vanishing elements4151366910.22108/ijgt.2014.3669ENThomasWolfOhio UniversityJournal Article20130904We characterize those groups $G$ and vector spaces $V$ such that $V$ is a faithful irreducible $G$-module and such that each $v$ in $V$ is centralized by a $G$-conjugate of a fixed non-identity element of the Fitting subgroup $F(G)$ of $G$. We also determine those $V$ and $G$ for which $V$ is a faithful quasi-primitive $G$-module and $F(G)$ has no regular orbit. We do use these to show in some cases that a non-vanishing element lies in $F(G)$.https://ijgt.ui.ac.ir/article_3669_cb1c4398181ca2cb64256d56ddd3c56c.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76503220140601Rational subsets of finite groups5355378010.22108/ijgt.2014.3780ENRogerAlperinSan Jose State UniversityJournal Article20130801We characterize the rational subsets of a finite group and discuss the relations to integral Cayley graphs.https://ijgt.ui.ac.ir/article_3780_18c76f677b0c46982874a6daadc10aec.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76503220140601Conjectures on the normal covering number of the finite symmetric and alternating groups5775378110.22108/ijgt.2014.3781ENDanielaBubboloniUniversity of FirenzeCheryl E.PraegerThe University of Western AustraliaPabloSpigaUniversity of Milano-BicoccaJournal Article20131010Let $\gamma(S_n)$ be the minimum number of proper subgroups $H_i,\ i=1, \dots, l $ of the symmetric group $S_n$ such that each element in $S_n$ lies in some conjugate of one of the $H_i.$ In this paper we conjecture that $$\gamma(S_n)=\frac{n}{2}\left(1-\frac{1}{p_1}\right) \left(1-\frac{1}{p_2}\right)+2,$$ where $p_1,p_2$ are the two smallest primes in the factorization of $n\in\mathbb{N}$ and $n$ is neither a prime power nor a product of two primes. Support for the conjecture is given by a previous result for $n=p_1^{\alpha_1}p_2^{\alpha_2},$ with $(\alpha_1,\alpha_2)\neq (1,1)$. We give further evidence by confirming the conjecture for integers <br />of the form $n=15q$ for an infinite set of primes $q$, and by reporting on a $ Magma$ computation. We make a similar conjecture for $\gamma(A_n)$, when $n$ is even, and provide a similar amount of evidence.https://ijgt.ui.ac.ir/article_3781_473bef8f89b0aadff416858b62a9ac31.pdf