University of Isfahan International Journal of Group Theory 2251-7650 2251-7669 2 4 2013 12 01 Unit group of algebra of circulant matrices 1 6 EN Rajendra Sharma Indian Institute of Technology Delhi rksharma@maths.iitd.ac.in Pooja Yadav Department of Mathematics, Kamla Nehru College, University of Delhi, Delhi iitd.pooja@gmail.com 10.22108/ijgt.2013.2643 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. Algebra,Unit Group,Circulant Matrices http://ijgt.ui.ac.ir/article_2643.html http://ijgt.ui.ac.ir/article_2643_33e935a9ca272310a728fc6513a0bbad.pdf
University of Isfahan International Journal of Group Theory 2251-7650 2251-7669 2 4 2013 12 01 Partially \$S\$-embedded minimal subgroups of finite groups 7 16 EN Tao Zhao School of Science, Shandong University of Technology zht198109@163.com Qingliang Zhang School of Sciences, Nantong University qingliangzhang@ntu.edu.cn 10.22108/ijgt.2013.2751 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.‎ s-permutable subgroup,partially S-embedded subgroup,nilpotent group,Formation http://ijgt.ui.ac.ir/article_2751.html http://ijgt.ui.ac.ir/article_2751_21631b0fa51b75065747f61c434fd5e4.pdf
University of Isfahan International Journal of Group Theory 2251-7650 2251-7669 2 4 2013 12 01 Noninner automorphisms of finite \$p\$-groups leaving the center elementwise fixed 17 20 EN Alireza Abdollahi University of Isfahan a.abdollahi@math.ui.ac.ir S. Mohsen Ghoraishi University of Isfahan m.ghoraishi@scu.ac.ir 10.22108/ijgt.2013.2761 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. Noninner automorphism,finite p-groups,the center http://ijgt.ui.ac.ir/article_2761.html http://ijgt.ui.ac.ir/article_2761_52bac5d4d3e407efd00cc7724a0d360e.pdf
University of Isfahan International Journal of Group Theory 2251-7650 2251-7669 2 4 2013 12 01 On supersolvability of finite groups with \$Bbb P\$-subnormal subgroups 21 29 EN Viktoryia Kniahina Gomel engineering institute of MES of Republic of Belarus knyagina@inbox.ru Victor Monakhov Department of Mathematics, Gomel F. Scorina State University Victor.Monakhov@gmail.com 10.22108/ijgt.2013.2835 In this paper we find systems of subgroups of a finite‎ ‎group‎, ‎which \$Bbb P\$-subnormality guarantees supersolvability‎ ‎of the whole group‎. Finite group,supersolvable group,\$\Bbb P\$-subnormal subgroup http://ijgt.ui.ac.ir/article_2835.html http://ijgt.ui.ac.ir/article_2835_846acc825bf3d7fa7d1fe37251836e69.pdf
University of Isfahan International Journal of Group Theory 2251-7650 2251-7669 2 4 2013 12 01 On the probability of being a \$2\$-Engel group 31 38 EN Ahmad Erfanian Ferdowsi University of Mashhad erfanian@math.um.ac.ir Mohammad Farrokhi Derakhshandeh Ghouchan Ferdowsi University of Mashhad 14999825@mmm.muroran-it.ac.jp 10.22108/ijgt.2013.2836 ‎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. Probability‎,‎2-Engel condition‎,3-metabelian http://ijgt.ui.ac.ir/article_2836.html http://ijgt.ui.ac.ir/article_2836_e178af16ad25afc5f74265a501ad63fb.pdf
University of Isfahan International Journal of Group Theory 2251-7650 2251-7669 2 4 2013 12 01 On finite C-tidy groups 39 41 EN Sekhar Jyoti Baishya North-Eastern Hill University sekharnehu@yahoo.com 10.22108/ijgt.2013.2838 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. Finite groups,cyclicizers,C-tidy groups http://ijgt.ui.ac.ir/article_2838.html http://ijgt.ui.ac.ir/article_2838_8f2b0e559e4fdea04fd0b7d3c5134624.pdf
University of Isfahan International Journal of Group Theory 2251-7650 2251-7669 2 4 2013 12 01 The \$n\$-ary adding machine and solvable groups 43 88 EN Josimar da Silva Rocha Instituto Federal de Educacao jsrocha74@gmail.com Said Sidki Universidade De Brasilia ssidki@gmail.com 10.22108/ijgt.2013.2871 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. Adding machine,Tree automorphisms,Automata,solvable groups http://ijgt.ui.ac.ir/article_2871.html http://ijgt.ui.ac.ir/article_2871_635f8d519f354a9c3204c92c000157ee.pdf