University of Isfahan International Journal of Group Theory 2251-7650 4 4 2015 12 01 Group rings for communications 1 23 5453 10.22108/ijgt.2015.5453 EN Ted Hurley National University of Ireland Galway Journal Article 2014 05 03 This is a survey of some recent applications of abstract‎ ‎algebra‎, ‎and in particular group rings‎, ‎to the communications' areas‎. https://ijgt.ui.ac.ir/article_5453_9f9342e7224465dd42f3537a6a7fe39a.pdf
University of Isfahan International Journal of Group Theory 2251-7650 4 4 2015 12 01 Groups of order \$p^8\$ and exponent \$p\$ 25 42 5758 10.22108/ijgt.2015.5758 EN Michael Vaughan-Lee Oxford University Mathematical Institute Journal Article 2014 06 12 ‎We prove that for \$p>7\$ there are ‎[‎ ‎p^{4}+2p^{3}+20p^{2}+147p+(3p+29)gcd (p-1,3)+5gcd (p-1,4)+1246‎ ‎] ‎groups of order \$p^{8}\$ with exponent \$p\$‎. ‎If \$P\$ is a group of order \$p^{8}\$‎ ‎and exponent \$p\$‎, ‎and if \$P\$ has class \$c>1\$ then \$P\$ is a descendant of \$ ‎P/gamma _{c}(P)\$‎. ‎For each group of exponent \$p\$ with order less than \$ ‎p^{8} \$ we calculate the number of descendants of order \$p^{8}\$ with‎ ‎exponent \$p\$‎. ‎In all but one case we are able to obtain a complete and‎ ‎irredundant list of the descendants‎. ‎But in the case of the three generator‎ ‎class two group of order \$p^{6}\$ and exponent \$p\$ (\$p>3\$)‎, ‎while we are able‎ ‎to calculate the number of descendants of order \$p^{8}\$‎, ‎we have not been‎ ‎able to obtain a list of the descendants‎. https://ijgt.ui.ac.ir/article_5758_388335a7f7fa07bfe83e3a007db2f69c.pdf
University of Isfahan International Journal of Group Theory 2251-7650 4 4 2015 12 01 Modules over group rings of groups with restrictions on the system of all proper subgroups 43 48 5504 10.22108/ijgt.2015.5504 EN Olga Dashkova Professor of the Branch of Moscow state university in Sevastopol Journal Article 2014 05 03 We consider the class \$mathfrak M\$ of \$bf R\$--modules where \$bf R\$ is an associative ring. Let \$A\$ be a module over a group ring \$bf R\$\$G\$, \$G\$ be a group and let \$mathfrak L(G)\$ be the set of all proper subgroups of \$G\$. We suppose that if \$H in mathfrak L(G)\$ then \$A/C_{A}(H)\$ belongs to \$mathfrak M\$. We investigate an \$bf R\$\$G\$--module \$A\$ such that \$G not = G'\$, \$C_{G}(A) = 1\$. We study the cases: 1) \$mathfrak M\$ is the class of all artinian \$bf R\$--modules, \$bf R\$ is either the ring of integers or the ring of \$p\$--adic integers; 2) \$mathfrak M\$ is the class of all finite \$bf R\$--modules, \$bf R\$ is an associative ring; 3) \$mathfrak M\$ is the class of all finite \$bf R\$--modules, \$bf R\$\$=F\$ is a finite field. https://ijgt.ui.ac.ir/article_5504_b2fda9c27d76f5bae4d99c57c8252f39.pdf
University of Isfahan International Journal of Group Theory 2251-7650 4 4 2015 12 01 Sylow like theorems for \$V(mathbb{Z}G)\$ 49 59 5452 10.22108/ijgt.2015.5452 EN Wolfgang Kimmerle University of Stuttgart Journal Article 2014 05 03 ‎The main part of this article is a survey on torsion subgroups of the unit group of‎ ‎an integral group ring‎. ‎It contains the major parts of my talk given at the‎ ‎conference‎ ‎"Groups,‎ ‎Group Rings and Related Topics‎" ‎at UAEU in Al Ain October 2013‎. ‎In the second part special emphasis is layed on \$p\$‎ - ‎subgroups and on the‎ ‎open question whether there is a Sylow like theorem in the‎ ‎normalized unit group of an integral group ring‎. ‎For specific classes of finite groups we prove that \$p\$‎ - ‎subgroups‎ ‎of the normalized unit group of its integral group rings \$V(mathbb{Z}G)\$ ‎are isomorphic to subgroups of \$G‎ .‎\$ In particular for \$p = 2\$ this is shown ‎when \$G\$ has abelian Sylow \$2\$‎ - ‎subgroups‎. ‎This extends results known‎ ‎for soluble groups to classes of groups which are not contained in the‎ ‎class of soluble groups‎. https://ijgt.ui.ac.ir/article_5452_1c109992064605dc78186ce51e795fb6.pdf
University of Isfahan International Journal of Group Theory 2251-7650 4 4 2015 12 01 On group rings and some of their applications to combinatorics and symmetric cryptography 61 74 5813 10.22108/ijgt.2015.5813 EN Claude Carlet Universities of Paris 8 and Paris 13 Yin Tan University of Waterloo Journal Article 2014 05 03 ‎We give a survey of recent applications of group rings to combinatorics and to cryptography‎, ‎including their use in the differential cryptanalysis of block ciphers‎. https://ijgt.ui.ac.ir/article_5813_aae52578d139936ffc37b6d71a0be349.pdf