University of IsfahanInternational Journal of Group Theory2251-76503420141201Restrictions on commutativity ratios in finite groups112457010.22108/ijgt.2014.4570ENRobertHeffernanUniversity of ConnecticutDesMacHaleUniversity College CorkAineNi SheCork Institute of TechnologyJournal Article20130905 We consider two commutativity ratios $\Pr(G)$ and $f(G)$ in a finite group $G$ and examine the properties of $G$ when these ratios are `large'. We show that if $\Pr(G) > \frac{7}{24}$, then $G$ is metabelian and we give threshold results in the cases where $G$ is insoluble and $G'$ is nilpotent. We also show that if $f(G) > \frac{1}{2}$, then $f(G) = \frac{n+1}{2n}$, for some natural number $n$.https://ijgt.ui.ac.ir/article_4570_55d0f1553f00e86de09233d4129f5a8f.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76503420141201The unit group of algebra of circulant matrices1316477610.22108/ijgt.2014.4776ENNehaMakhijaniIndian Institute of Technology Delhi
Hauz Khas, New Delhi-110016
IndiaR. K.SharmaIndian Institute of Technology Delhi
Hauz Khas, New Delhi
IndiaJ. B.SrivastavaIndian Institute of Technology Delhi
Hauz Khas, New Delhi
IndiaJournal Article20131024Let $Cr_{n}(F)$ denote the algebra of $n\times n$ circulant matrices over the field $F$. In this paper, we study the unit group of $Cr_{n}(\mathbb{F}_{p^{m}})$, where $\mathbb{F}_{p^{m}}$ denotes the Galois field of order $p^{m},~p$ prime.https://ijgt.ui.ac.ir/article_4776_76fd6d2530a88ac6184b7c4c0c57fca7.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76503420141201On weakly $SS$-quasinormal and hypercyclically embedded properties of finite groups1725495010.22108/ijgt.2014.4950ENTaoZhaoSchool of Science, Shandong University of TechnologyJournal Article20140216A subgroup $H$ is said to be $s$-permutable in a group $G$, if $HP=PH$ holds for every Sylow subgroup $P$ of $G$. If there exists a subgroup $B$ of $G$ such that $HB=G$ and $H$ permutes with every Sylow subgroup of $B$, then $H$ is said to be $SS$-quasinormal in $G$. In this paper, we say that $H$ is a weakly $SS$-quasinormal subgroup of $G$, if there is a normal subgroup $T$ of $G$ such that $HT$ is $s$-permutable and $H\cap T$ is $SS$-quasinormal in $G$. By assuming that some subgroups of $G$ with prime power order have the weakly $SS$-quasinormal properties, we get some new characterizations about the hypercyclically embedded subgroups of $G$. A series of known results in the literature are unified and generalized.https://ijgt.ui.ac.ir/article_4950_c0915a41877e3a4bb1db406fbaca42cf.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76503420141201On zero patterns of characters of finite groups2731495210.22108/ijgt.2014.4952ENJinshanZhangSchool of Science, Sichuan University of
Science and Engineering, Zigong, 643000, P. R. ChinaGuangjuZengSichuan University of Science and EngineeringZhencaiShenChina Agricultural UniversityJournal Article20131030The aim of this note is to characterize the finite groups in which all non-linear irreducible characters have distinct zero entries number.https://ijgt.ui.ac.ir/article_4952_63eb74c1c94bc55ca2353308a1051eba.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76503420141201A note on the Normalizer of sylow 2-subgroup of special linear group SL2(pf)3336497610.22108/ijgt.2014.4976ENJiangtaoShiYantai UniversityJournal Article20131122Let $G={\rm SL}_2(p^f)$ be a special linear group and $P$ be a Sylow $2$-subgroup of $G$, where $p$ is a prime and $f$ is a positive integer such that $p^f>3$. By $N_G(P)$ we denote the normalizer of $P$ in $G$. In this paper, we show that $N_G(P)$ is nilpotent (or $2$-nilpotent, or supersolvable) if and only if $p^{2f}\equiv 1\,({\rm mod}\,16)$.https://ijgt.ui.ac.ir/article_4976_a69c9b523546d6cc0812f1d9027240e7.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76503420141201On one class of modules over group rings with finiteness restrictions3746508710.22108/ijgt.2014.5087ENOlgaDashkovaProfessor of the Branch of Moscow state university in SevastopolJournal Article20140323The author studies the $\bf R$$G$-module $A$ such that $\bf R$ is an associative ring, a group $G$ has infinite section $p$-rank (or infinite 0-rank), $C_{G}(A)=1$, and for every proper subgroup $H$ of infinite section $p$-rank (or infinite 0-rank respectively) the quotient module $A/C_{A}(H)$ is a finite $\bf R$-module. It is proved that if the group $G$ under consideration is locally soluble then $G$ is a soluble group and $A/C_{A}(G)$ is a finite $\bf R$-module. https://ijgt.ui.ac.ir/article_5087_ca4189aa5efbaeed67562c6122922f8a.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76503420141201Quasirecognition by prime graph of finite simple Groups 2Dn(3)4756525410.22108/ijgt.2014.5254ENBehroozKhosraviHosseinMoradiAmirkabir University of TechnologyJournal Article20130418Let $G$ be a finite group. In [Ghasemabadi et al., characterizations of the simple group ${}^2D_n(3)$ by prime graph and spectrum, Monatsh Math., 2011] it is proved that if $n$ is odd, then ${}^2D _n(3)$ is recognizable by prime graph and also by element orders. In this paper we prove that if $n$ is even, then $D={}^2D_{n}(3)$ is quasirecognizable by prime graph, i.e. every finite group $G$ with $\Gamma(G)=\Gamma(D)$ has a unique nonabelian composition factor and this factor is isomorphic to $D$.https://ijgt.ui.ac.ir/article_5254_b31e2bb7e4d6f7188c9fd129dd78758f.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76503420141201A note on fixed points of automorphisms of infinite groups5761534210.22108/ijgt.2014.5342ENFrancescoDe GiovanniUniversity of Napoli Federico IIMartin L.NewellNational University of IrelandAlessioRussoSeconda Universita di NapoliJournal Article20140415Motivated by a celebrated theorem of Schur, we show that if $\Gamma$ is a normal subgroup of the full automorphism group $Aut(G)$ of a group $G$ such that $Inn(G)$ is contained in $\Gamma$ and $Aut(G)/\Gamma$ has no uncountable abelian subgroups of prime exponent, then $[G,\Gamma]$ is finite, provided that the subgroup consisting of all elements of $G$ fixed by $\Gamma$ has finite index. Some applications of this result are also given.https://ijgt.ui.ac.ir/article_5342_1e6c5c18b97f38824f43a2febfd71900.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76503420141201Symmetry classes of polynomials associated with the direct product of permutation groups6369547910.22108/ijgt.2014.5479ENEsmaeilBabaeiSahand University of technologyYousefZamaniSahand University of TechnologyJournal Article20140130Let $G_{i} $ be a subgroup of $ S_{m_{i}} ,\ 1 \leq i \leq k$. Suppose $\chi_{i}$ is an irreducible complex character of $G_{i}$. We consider $ G_{1}\times \cdots \times G_{k} $ as subgroup of $ S_{m} $, where $ m=m_{1}+\cdots +m_{k} $. In this paper, we give a formula for the dimension of $H_{d}(G_{1}\times \cdots \times G_{k}, \chi_{1}\times\cdots \times \chi_{k})$ and investigate the existence of an o-basis of this type of classes.https://ijgt.ui.ac.ir/article_5479_0495fb15f251988634840c9c7812f01e.pdf