ORIGINAL_ARTICLE Unit group of algebra of circulant matrices 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 2013-12-01T11:23:20 2019-05-24T11:23:20 1 6 10.22108/ijgt.2013.2643 Algebra Unit Group Circulant Matrices Rajendra Sharma rksharma@maths.iitd.ac.in true 1 Indian Institute of Technology Delhi Indian Institute of Technology Delhi Indian Institute of Technology Delhi LEAD_AUTHOR Pooja Yadav iitd.pooja@gmail.com true 2 Department of Mathematics, Kamla Nehru College, University of Delhi, Delhi Department of Mathematics, Kamla Nehru College, University of Delhi, Delhi Department of Mathematics, Kamla Nehru College, University of Delhi, Delhi AUTHOR
ORIGINAL_ARTICLE Partially $S$-embedded minimal subgroups of finite groups 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 $H\cap T\leq H_{\overline{s}G}$‎, ‎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 2013-12-01T11:23:20 2019-05-24T11:23:20 7 16 10.22108/ijgt.2013.2751 s-permutable subgroup partially S-embedded subgroup nilpotent group Formation 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 Qingliang Zhang qingliangzhang@ntu.edu.cn true 2 School of Sciences, Nantong University School of Sciences, Nantong University School of Sciences, Nantong University AUTHOR
ORIGINAL_ARTICLE Noninner automorphisms of finite $p$-groups leaving the center elementwise fixed 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 2013-12-01T11:23:20 2019-05-24T11:23:20 17 20 10.22108/ijgt.2013.2761 Noninner automorphism finite p-groups the center Alireza Abdollahi a.abdollahi@math.ui.ac.ir true 1 University of Isfahan University of Isfahan University of Isfahan LEAD_AUTHOR S. Mohsen Ghoraishi m.ghoraishi@scu.ac.ir true 2 University of Isfahan University of Isfahan University of Isfahan AUTHOR
ORIGINAL_ARTICLE On supersolvability of finite groups with $\Bbb P$-subnormal subgroups 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 2013-12-01T11:23:20 2019-05-24T11:23:20 21 29 10.22108/ijgt.2013.2835 Finite group supersolvable group $Bbb P$-subnormal subgroup Viktoryia Kniahina knyagina@inbox.ru true 1 Gomel engineering institute of MES of Republic of Belarus Gomel engineering institute of MES of Republic of Belarus Gomel engineering institute of MES of Republic of Belarus LEAD_AUTHOR Victor Monakhov Victor.Monakhov@gmail.com true 2 Department of Mathematics, Gomel F. Scorina State University Department of Mathematics, Gomel F. Scorina State University Department of Mathematics, Gomel F. Scorina State University AUTHOR
ORIGINAL_ARTICLE On the probability of being a $2$-Engel group ‎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 $E_G(x)=\{y\in G:[y,x,x]=1\}$ are subgroups of $G$ for‎ ‎all $x\in G$‎. ‎Also the given examples illustrate that all the‎ ‎bounds are sharp‎. http://ijgt.ui.ac.ir/article_2836_e178af16ad25afc5f74265a501ad63fb.pdf 2013-12-01T11:23:20 2019-05-24T11:23:20 31 38 10.22108/ijgt.2013.2836 Probability‎ ‎2-Engel condition‎ 3-metabelian Ahmad Erfanian erfanian@math.um.ac.ir true 1 Ferdowsi University of Mashhad Ferdowsi University of Mashhad Ferdowsi University of Mashhad AUTHOR Mohammad Farrokhi Derakhshandeh Ghouchan 14999825@mmm.muroran-it.ac.jp true 2 Ferdowsi University of Mashhad Ferdowsi University of Mashhad Ferdowsi University of Mashhad LEAD_AUTHOR
ORIGINAL_ARTICLE On finite C-tidy groups 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 2013-12-01T11:23:20 2019-05-24T11:23:20 39 41 10.22108/ijgt.2013.2838 Finite groups cyclicizers C-tidy groups Sekhar Baishya sekharnehu@yahoo.com true 1 North-Eastern Hill University North-Eastern Hill University North-Eastern Hill University LEAD_AUTHOR
ORIGINAL_ARTICLE The $n$-ary adding machine and solvable groups 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 $\left( 0,1‎, ‎\dots‎, ‎n-1\right)$‎. ‎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 2013-12-01T11:23:20 2019-05-24T11:23:20 43 88 10.22108/ijgt.2013.2871 Adding machine Tree automorphisms Automata solvable groups Josimar da Silva Rocha jsrocha74@gmail.com true 1 Instituto Federal de Educacao Instituto Federal de Educacao Instituto Federal de Educacao AUTHOR Said Sidki ssidki@gmail.com true 2 Universidade De Brasilia Universidade De Brasilia Universidade De Brasilia LEAD_AUTHOR