University of Isfahan International Journal of Group Theory 2251-7650 2 4 2013 12 01 Unit group of algebra of circulant matrices 1 6 2643 10.22108/ijgt.2013.2643 EN Rajendra Sharma Indian Institute of Technology Delhi Pooja Yadav Department of Mathematics, Kamla Nehru College, University of Delhi, Delhi Journal Article 2012 09 28 Let \$Cr_n(F_p)\$ denote the algebra of \$n times n\$ circulant‎ ‎matrices over \$F_p\$‎, ‎the finite field of order \$p\$ a prime‎. ‎The‎ ‎order of the unit groups \$mathcal{U}(Cr_3(F_p))\$‎, ‎\$mathcal{U}(Cr_4(F_p))\$ and \$mathcal{U}(Cr_5(F_p))\$ of algebras of‎ ‎circulant matrices over \$F_p\$ are computed‎. http://ijgt.ui.ac.ir/article_2643_33e935a9ca272310a728fc6513a0bbad.pdf
University of Isfahan International Journal of Group Theory 2251-7650 2 4 2013 12 01 Partially \$S\$-embedded minimal subgroups of finite groups 7 16 2751 10.22108/ijgt.2013.2751 EN Tao Zhao School of Science, Shandong University of Technology Qingliang Zhang School of Sciences, Nantong University Journal Article 2013 02 13 Suppose that \$H\$ is a subgroup of \$G\$‎, ‎then \$H\$ is said to be‎ ‎\$s\$-permutable in \$G\$‎, ‎if \$H\$ permutes with every Sylow subgroup of‎ ‎\$G\$‎. ‎If \$HP=PH\$ hold for every Sylow subgroup \$P\$ of \$G\$ with \$(|P|‎, ‎|H|)=1\$)‎, ‎then \$H\$ is called an \$s\$-semipermutable subgroup of \$G\$‎. ‎In this paper‎, ‎we say that \$H\$ is partially \$S\$-embedded in \$G\$ if‎ ‎\$G\$ has a normal subgroup \$T\$ such that \$HT\$ is \$s\$-permutable in‎ ‎\$G\$ and \$Hcap Tleq H_{overline{s}G}\$‎, ‎where \$H_{overline{s}G}\$‎ ‎is generated by all \$s\$-semipermutable subgroups of \$G\$ contained in‎ ‎\$H\$‎. ‎We investigate the influence of some partially \$S\$-embedded‎ ‎minimal subgroups on the nilpotency and supersolubility of a finite‎ ‎group \$G\$‎. ‎A series of known results in the literature are unified‎ ‎and generalized.‎ http://ijgt.ui.ac.ir/article_2751_21631b0fa51b75065747f61c434fd5e4.pdf
University of Isfahan International Journal of Group Theory 2251-7650 2 4 2013 12 01 Noninner automorphisms of finite \$p\$-groups leaving the center elementwise fixed 17 20 2761 10.22108/ijgt.2013.2761 EN Alireza Abdollahi University of Isfahan S. Mohsen Ghoraishi University of Isfahan Journal Article 2013 02 25 A longstanding conjecture asserts that every finite nonabelian \$p\$-group admits a noninner automorphism of order \$p\$. Let \$G\$ be a finite nonabelian \$p\$-group. It is known that if \$G\$ is regular or of nilpotency class \$2\$ or the commutator subgroup of \$G\$ is cyclic, or \$G/Z(G)\$ is powerful, then \$G\$ has a noninner automorphism of order \$p\$ leaving either the center \$Z(G)\$ or the Frattini subgroup \$Phi(G)\$ of \$G\$ elementwise fixed. In this note, we prove that the latter noninner automorphism can be chosen so that it leaves \$Z(G)\$ elementwise fixed. http://ijgt.ui.ac.ir/article_2761_52bac5d4d3e407efd00cc7724a0d360e.pdf
University of Isfahan International Journal of Group Theory 2251-7650 2 4 2013 12 01 On supersolvability of finite groups with \$Bbb P\$-subnormal subgroups 21 29 2835 10.22108/ijgt.2013.2835 EN Viktoryia Kniahina Gomel engineering institute of MES of Republic of Belarus Victor Monakhov Department of Mathematics, Gomel F. Scorina State University Journal Article 2012 12 01 In this paper we find systems of subgroups of a finite‎ ‎group‎, ‎which \$Bbb P\$-subnormality guarantees supersolvability‎ ‎of the whole group‎. http://ijgt.ui.ac.ir/article_2835_846acc825bf3d7fa7d1fe37251836e69.pdf
University of Isfahan International Journal of Group Theory 2251-7650 2 4 2013 12 01 On the probability of being a \$2\$-Engel group 31 38 2836 10.22108/ijgt.2013.2836 EN Ahmad Erfanian Ferdowsi University of Mashhad Mohammad Farrokhi Derakhshandeh Ghouchan Ferdowsi University of Mashhad Journal Article 2013 03 12 ‎Let \$G\$ be a finite group and \$d_2(G)\$ denotes the probability‎ ‎that \$[x,y,y]=1\$ for randomly chosen elements \$x,y\$ of \$G\$‎. ‎We‎ ‎will obtain lower and upper bounds for \$d_2(G)\$ in the case where‎ ‎the sets \$E_G(x)={yin G:[y,x,x]=1}\$ are subgroups of \$G\$ for‎ ‎all \$xin G\$‎. ‎Also the given examples illustrate that all the‎ ‎bounds are sharp‎. http://ijgt.ui.ac.ir/article_2836_e178af16ad25afc5f74265a501ad63fb.pdf
University of Isfahan International Journal of Group Theory 2251-7650 2 4 2013 12 01 On finite C-tidy groups 39 41 2838 10.22108/ijgt.2013.2838 EN Sekhar Jyoti Baishya North-Eastern Hill University Journal Article 2013 01 30 A group \$G\$ is said to be a C-tidy group if for every element \$x in G setminus K(G)\$‎, ‎the set \$Cyc(x)=lbrace y in G mid langle x‎, ‎y rangle ; {rm is ; cyclic} rbrace\$ is a cyclic subgroup of \$G\$‎, ‎where \$K(G)=underset{x in G}bigcap Cyc(x)\$‎. ‎In this short note we determine the structure of finite C-tidy groups‎. http://ijgt.ui.ac.ir/article_2838_8f2b0e559e4fdea04fd0b7d3c5134624.pdf
University of Isfahan International Journal of Group Theory 2251-7650 2 4 2013 12 01 The \$n\$-ary adding machine and solvable groups 43 88 2871 10.22108/ijgt.2013.2871 EN Josimar da Silva Rocha Instituto Federal de Educacao Said Sidki Universidade De Brasilia Journal Article 2013 04 20 We describe under various conditions abelian subgroups of the automorphism‎ ‎group \$mathrm{Aut}(T_{n})\$ of the regular \$n\$-ary tree \$T_{n}\$‎, ‎which are‎ ‎normalized by the \$n\$-ary adding machine \$tau =(e‎, ‎dots‎, ‎e,tau )sigma _{tau‎ ‎}\$ where \$sigma _{tau }\$ is the \$n\$-cycle \$left( 0,1‎, ‎dots‎, ‎n-1right) \$‎. ‎As‎ ‎an application‎, ‎for \$n=p\$ a prime number‎, ‎and for \$n=4\$‎, ‎we prove that‎ ‎every soluble subgroup of \$mathrm{Aut}(T_{n})\$‎, ‎containing \$tau \$ is an extension of a torsion-free metabelian group by a‎ ‎finite group‎. http://ijgt.ui.ac.ir/article_2871_635f8d519f354a9c3204c92c000157ee.pdf