Group rings for communications Ted Hurley National University of Ireland Galway author text article 2015 eng This is a survey of some recent applications of abstract‎ ‎algebra‎, ‎and in particular group rings‎, ‎to the communications' areas‎. International Journal of Group Theory University of Isfahan 2251-7650 4 v. 4 no. 2015 1 23 http://ijgt.ui.ac.ir/article_5453_9f9342e7224465dd42f3537a6a7fe39a.pdf dx.doi.org/10.22108/ijgt.2015.5453 Groups of order $p^8$ and exponent $p$ Michael Vaughan-Lee Oxford University Mathematical Institute author text article 2015 eng ‎We prove that for $p>7$ there are ‎$‎ ‎p^{4}+2p^{3}+20p^{2}+147p+(3p+29)\gcd (p-1,3)+5\gcd (p-1,4)+1246‎ ‎$ ‎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. International Journal of Group Theory University of Isfahan 2251-7650 4 v. 4 no. 2015 25 42 http://ijgt.ui.ac.ir/article_5758_388335a7f7fa07bfe83e3a007db2f69c.pdf dx.doi.org/10.22108/ijgt.2015.5758 Modules over group rings of groups with restrictions on the system of all proper subgroups Olga Dashkova Professor of the Branch of Moscow state university in Sevastopol author text article 2015 eng 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. International Journal of Group Theory University of Isfahan 2251-7650 4 v. 4 no. 2015 43 48 http://ijgt.ui.ac.ir/article_5504_b2fda9c27d76f5bae4d99c57c8252f39.pdf dx.doi.org/10.22108/ijgt.2015.5504 Sylow like theorems for $V(\mathbb{Z}G)$ Wolfgang Kimmerle University of Stuttgart author text article 2015 eng ‎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. International Journal of Group Theory University of Isfahan 2251-7650 4 v. 4 no. 2015 49 59 http://ijgt.ui.ac.ir/article_5452_1c109992064605dc78186ce51e795fb6.pdf dx.doi.org/10.22108/ijgt.2015.5452 On group rings and some of their applications to combinatorics and symmetric cryptography Claude Carlet Universities of Paris 8 and Paris 13 author Yin Tan University of Waterloo author text article 2015 eng ‎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. International Journal of Group Theory University of Isfahan 2251-7650 4 v. 4 no. 2015 61 74 http://ijgt.ui.ac.ir/article_5813_aae52578d139936ffc37b6d71a0be349.pdf dx.doi.org/10.22108/ijgt.2015.5813