ORIGINAL_ARTICLE Restrictions on commutativity ratios in finite groups  ‎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 $n$‎. http://ijgt.ui.ac.ir/article_4570_55d0f1553f00e86de09233d4129f5a8f.pdf 2014-12-01T11:23:20 2019-05-24T11:23:20 1 12 10.22108/ijgt.2014.4570 commutativity ratios commuting probability Finite groups Robert Heffernan robert.heffernan@uconn.edu true 1 University of Connecticut University of Connecticut University of Connecticut LEAD_AUTHOR Des MacHale d.machale@ucc.ie true 2 University College Cork University College Cork University College Cork AUTHOR Aine Ni She aine.nishe@cit.ie true 3 Cork Institute of Technology Cork Institute of Technology Cork Institute of Technology AUTHOR
ORIGINAL_ARTICLE The unit group of algebra of circulant matrices Let $Cr_{n}(F)$ 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. http://ijgt.ui.ac.ir/article_4776_76fd6d2530a88ac6184b7c4c0c57fca7.pdf 2014-12-01T11:23:20 2019-05-24T11:23:20 13 16 10.22108/ijgt.2014.4776 group algebra Unit Group Circulant Matrices Neha Makhijani nehamakhijani@gmail.com true 1 Indian Institute of Technology Delhi Hauz Khas, New Delhi-110016 India Indian Institute of Technology Delhi Hauz Khas, New Delhi-110016 India Indian Institute of Technology Delhi Hauz Khas, New Delhi-110016 India LEAD_AUTHOR R. K. Sharma rksharmaiitd@gmail.com true 2 Indian Institute of Technology Delhi Hauz Khas, New Delhi India Indian Institute of Technology Delhi Hauz Khas, New Delhi India Indian Institute of Technology Delhi Hauz Khas, New Delhi India AUTHOR J. B. Srivastava jbsrivas@gmail.com true 3 Indian Institute of Technology Delhi Hauz Khas, New Delhi India Indian Institute of Technology Delhi Hauz Khas, New Delhi India Indian Institute of Technology Delhi Hauz Khas, New Delhi India AUTHOR
ORIGINAL_ARTICLE On weakly $SS$-quasinormal and hypercyclically embedded properties of finite groups A 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. http://ijgt.ui.ac.ir/article_4950_c0915a41877e3a4bb1db406fbaca42cf.pdf 2014-12-01T11:23:20 2019-05-24T11:23:20 17 25 10.22108/ijgt.2014.4950 ‎$s$-permutable‎ ‎weakly $SS$-quasinormal‎ $p$-nilpotent‎ ‎hypercyclically embedded Tao Zhao zht198109@163.com true 1 School of Science, Shandong University of Technology School of Science, Shandong University of Technology School of Science, Shandong University of Technology LEAD_AUTHOR
ORIGINAL_ARTICLE On zero patterns of characters of finite groups The aim of this note is to characterize the finite‎ ‎groups in which all non-linear irreducible characters have distinct zero entries number‎. http://ijgt.ui.ac.ir/article_4952_63eb74c1c94bc55ca2353308a1051eba.pdf 2014-12-01T11:23:20 2019-05-24T11:23:20 27 31 10.22108/ijgt.2014.4952 Finite groups characters zeros of characters Jinshan Zhang zjscdut@163.com true 1 School of Science, Sichuan University of Science and Engineering, Zigong, 643000, P. R. China School of Science, Sichuan University of Science and Engineering, Zigong, 643000, P. R. China School of Science, Sichuan University of Science and Engineering, Zigong, 643000, P. R. China LEAD_AUTHOR Guangju Zeng weiwei@suse.edu.cn true 2 Sichuan University of Science and Engineering Sichuan University of Science and Engineering Sichuan University of Science and Engineering AUTHOR Zhencai Shen true 3 China Agricultural University China Agricultural University China Agricultural University AUTHOR
ORIGINAL_ARTICLE A note on the normalizer of Sylow $2$-subgroup of special linear‎ ‎group ${\rm SL}_2(p^f)$ Let $G={\rm SL}_2(p^f)$ 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 $p^{2f}\equiv‎ ‎1\,({\rm mod}\,16)$‎. http://ijgt.ui.ac.ir/article_4976_a69c9b523546d6cc0812f1d9027240e7.pdf 2014-12-01T11:23:20 2019-05-24T11:23:20 33 36 10.22108/ijgt.2014.4976 special linear group Sylow subgroup normalizer nilpotent supersolvable Jiangtao Shi jiangtaoshi@126.com true 1 Yantai University Yantai University Yantai University LEAD_AUTHOR
ORIGINAL_ARTICLE On one class of modules over group rings with finiteness restrictions The 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. ‎ http://ijgt.ui.ac.ir/article_5087_ca4189aa5efbaeed67562c6122922f8a.pdf 2014-12-01T11:23:20 2019-05-24T11:23:20 37 46 10.22108/ijgt.2014.5087 group ring linear group module Olga Dashkova odashkova@yandex.ru true 1 Professor of the Branch of Moscow state university in Sevastopol Professor of the Branch of Moscow state university in Sevastopol Professor of the Branch of Moscow state university in Sevastopol LEAD_AUTHOR
ORIGINAL_ARTICLE Quasirecognition by prime graph of finite simple groups ${}^2D_n(3)$ ‎Let $G$ 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 ‎$D$‎. http://ijgt.ui.ac.ir/article_5254_b31e2bb7e4d6f7188c9fd129dd78758f.pdf 2014-12-01T11:23:20 2019-05-24T11:23:20 47 56 10.22108/ijgt.2014.5254 Prime graph simple group linear group quasirecognition Behrooz Khosravi bkhosravi@aut.ac.ir true 1 LEAD_AUTHOR Hossein Moradi khosravibbb@yahoo.com true 2 Amirkabir University of Technology Amirkabir University of Technology Amirkabir University of Technology AUTHOR
ORIGINAL_ARTICLE A note on fixed points of automorphisms of infinite groups ‎Motivated 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.‎ http://ijgt.ui.ac.ir/article_5342_1e6c5c18b97f38824f43a2febfd71900.pdf 2014-12-01T11:23:20 2019-05-24T11:23:20 57 61 10.22108/ijgt.2014.5342 automorphism group Schur's theorem absolute centre Francesco de Giovanni degiovan@unina.it true 1 University of Napoli Federico II University of Napoli Federico II University of Napoli Federico II LEAD_AUTHOR Martin L. Newell martin.newell@nuigalway.ie true 2 National University of Ireland National University of Ireland National University of Ireland AUTHOR Alessio Russo alessio.russo@unina2.it true 3 Seconda Universita di Napoli Seconda Universita di Napoli Seconda Universita di Napoli AUTHOR
ORIGINAL_ARTICLE Symmetry classes of polynomials associated with the ‎direct ‎product of permutation groups ‎Let $G_{i}$ 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. http://ijgt.ui.ac.ir/article_5479_0495fb15f251988634840c9c7812f01e.pdf 2014-12-01T11:23:20 2019-05-24T11:23:20 63 69 10.22108/ijgt.2014.5479 Symmetric polynomials symmetry class of polynomials‎ ‎orthogonal basis ‎permutaion groups‎ ‎complex characters Esmaeil Babaei e_babaei@sut.ac.ir true 1 Sahand University of technology Sahand University of technology Sahand University of technology AUTHOR Yousef Zamani zamani@sut.ac.ir true 2 Sahand University of Technology Sahand University of Technology Sahand University of Technology LEAD_AUTHOR