University of IsfahanInternational Journal of Group Theory2251-76504420151201Group rings for communications123545310.22108/ijgt.2015.5453ENTedHurleyNational University of Ireland GalwayJournal Article20140503This 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.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76504420151201Groups of order p8 and exponent p2542575810.22108/ijgt.2015.5758ENMichaelVaughan-LeeOxford University
Mathematical InstituteJournal Article20140612We 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.https://ijgt.ui.ac.ir/article_5758_388335a7f7fa07bfe83e3a007db2f69c.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76504420151201Modules over group rings of groups with restrictions on the system of all proper subgroups4348550410.22108/ijgt.2015.5504ENOlgaDashkovaProfessor of the Branch of Moscow state university in SevastopolJournal Article20140503We 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.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76504420151201Sylow like theorems for V (ℤG)4959545210.22108/ijgt.2015.5452ENWolfgangKimmerleUniversity of StuttgartJournal Article20140503The 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.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76504420151201On group rings and some of their applications to combinatorics and cryptography6174581310.22108/ijgt.2015.5813ENClaudeCarletUniversities of Paris 8 and Paris 13YinTanUniversity of WaterlooJournal Article20140503We 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