University of Isfahan International Journal of Group Theory 2251-7650 3 4 2014 12 01 Restrictions on commutativity ratios in finite groups 1 12 4570 10.22108/ijgt.2014.4570 EN Robert Heffernan University of Connecticut Des MacHale University College Cork Aine Ni She Cork Institute of Technology Journal Article 2013 09 05  ‎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
University of Isfahan International Journal of Group Theory 2251-7650 3 4 2014 12 01 The unit group of algebra of circulant matrices 13 16 4776 10.22108/ijgt.2014.4776 EN Neha Makhijani Indian Institute of Technology Delhi Hauz Khas, New Delhi-110016 India R. K. Sharma Indian Institute of Technology Delhi Hauz Khas, New Delhi India J. B. Srivastava Indian Institute of Technology Delhi Hauz Khas, New Delhi India Journal Article 2013 10 24 Let \$Cr_{n}(F)\$ denote the algebra of \$ntimes 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
University of Isfahan International Journal of Group Theory 2251-7650 3 4 2014 12 01 On weakly \$SS\$-quasinormal and hypercyclically embedded properties of finite groups 17 25 4950 10.22108/ijgt.2014.4950 EN Tao Zhao School of Science, Shandong University of Technology Journal Article 2014 02 16 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 \$Hcap 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
University of Isfahan International Journal of Group Theory 2251-7650 3 4 2014 12 01 On zero patterns of characters of finite groups 27 31 4952 10.22108/ijgt.2014.4952 EN Jinshan Zhang School of Science, Sichuan University of Science and Engineering, Zigong, 643000, P. R. China Guangju Zeng Sichuan University of Science and Engineering Zhencai Shen China Agricultural University Journal Article 2013 10 30 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
University of Isfahan International Journal of Group Theory 2251-7650 3 4 2014 12 01 A note on the normalizer of Sylow \$2\$-subgroup of special linear‎ ‎group \${rm SL}_2(p^f)\$ 33 36 4976 10.22108/ijgt.2014.4976 EN Jiangtao Shi Yantai University Journal Article 2013 11 22 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
University of Isfahan International Journal of Group Theory 2251-7650 3 4 2014 12 01 On one class of modules over group rings with finiteness restrictions 37 46 5087 10.22108/ijgt.2014.5087 EN Olga Dashkova Professor of the Branch of Moscow state university in Sevastopol Journal Article 2014 03 23 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
University of Isfahan International Journal of Group Theory 2251-7650 3 4 2014 12 01 Quasirecognition by prime graph of finite simple groups \${}^2D_n(3)\$ 47 56 5254 10.22108/ijgt.2014.5254 EN Behrooz Khosravi Hossein Moradi Amirkabir University of Technology Journal Article 2013 04 18 ‎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
University of Isfahan International Journal of Group Theory 2251-7650 3 4 2014 12 01 A note on fixed points of automorphisms of infinite groups 57 61 5342 10.22108/ijgt.2014.5342 EN Francesco de Giovanni University of Napoli Federico II Martin L. Newell National University of Ireland Alessio Russo Seconda Universita di Napoli Journal Article 2014 04 15 ‎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
University of Isfahan International Journal of Group Theory 2251-7650 3 4 2014 12 01 Symmetry classes of polynomials associated with the ‎direct ‎product of permutation groups 63 69 5479 10.22108/ijgt.2014.5479 EN Esmaeil Babaei Sahand University of technology Yousef Zamani Sahand University of Technology Journal Article 2014 01 30 ‎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}timescdots 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