University of IsfahanInternational Journal of Group Theory2251-76502120121201Proceedings of Ischia Group Theory 20122367110.22108/ijgt.2012.23671ENJournal Article20120126Proceedings of Ischia Group Theory 2012https://ijgt.ui.ac.ir/article_23671_9b7f1f4ca047f9e4b904319a941db299.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76502120130301Centralizers in simple locally finite groups110152110.22108/ijgt.2013.1521ENMahmutKuzucuoğluJournal Article20120420This is a survey article on centralizers of finite subgroups in locally finite, simple groups or LFS-groups as we will call them. We mention some of the open problems about centralizers of subgroups in LFS-groups and applications of the known information about the centralizers of subgroups to the structure of the locally finite group. We also prove the following: Let $G$ be a countably infinite non-linear LFS-group with a Kegel sequence $\mathcal{K}=\{(G_i,N_i)\ |\ \ i\in \mathbf{N}\ \}$. If there exists an upper bound for $\{ |N_i| \ | \ \ i\in \mathbf{N}\ \}$, then for any finite semisimple subgroup $F$ in $G$ the subgroup $C_G(F)$ has elements of order $p_i$ for infinitely many distinct prime $p_i$. In particular $C_G(F)$ is an infinite group. This answers Hartley's question provided that there exists a bound on $\{ |N_i| \ | \ \ i\in \mathbf{N}\ \}$https://ijgt.ui.ac.ir/article_1521_f96e46ddc879945b9b1ada62f715c862.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76502120130301Replacement and zig-zag products, Cayley graphs and Lamplighter random walk1135193210.22108/ijgt.2013.1932ENAlfredoDonnoUniversità di Roma "La Sapienza"Journal Article20120924We investigate two constructions - the replacement and the zig-zag product of graphs - describing several fascinating connections with Combinatorics, via the notion of expander graph, Group Theory, via the notion of semidirect product and Cayley graph, and with Markov chains, via the Lamplighter random walk. Many examples are provided.https://ijgt.ui.ac.ir/article_1932_cab6bdc876cc1f685e588bddab0243fc.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76502120130301Groups with all subgroups permutable or soluble3743200810.22108/ijgt.2013.2008ENMartynDixonUniversity of AlabamaZekeriyaKaratasUniversity of GeorgiaJournal Article20121029In this paper, we consider locally graded groups in which every non-permutable subgroup is soluble of bounded derived length.https://ijgt.ui.ac.ir/article_2008_2258282ce9f951b8bdbf8f4d28f3ad05.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76502120130301Factorizing profinite groups into two abelian subgroups4547234110.22108/ijgt.2013.2341ENWolfgangHerfortUniversity of TechnologyJournal Article20121101We prove that the class of profinite groups $G$ that have a factorization $G=AB$ with $A$ and $B$ abelian closed subgroups, is closed under taking inverse limits of surjective inverse systems. This is a generalization of a recent result by K. H. Hofmann and F. G. Russo. As an application we reprove their generalization of Iwasawa's structure theorem for quasihamiltonian pro-$p$ groups.https://ijgt.ui.ac.ir/article_2341_935b81d6227dda83e4ad6d3d1bc07f37.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76502120130301Cocharacters of upper triangular matrices4977239210.22108/ijgt.2013.2392ENLucioCentroneUniversita; degli Studi di Bari, II facolta; di scienze, TarantoJournal Article20120717We survey some recent results on cocharacters of upper triangular matrices. In particular, we deal both with ordinary and graded cocharacter sequence; we list the principal combinatorial results; we show different techniques in order to solve similar problems.https://ijgt.ui.ac.ir/article_2392_e062303d2c7de58331c72dbeafbb1519.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76502120130301Linear analogues of theorems of Schur, Baer and Hall7989244110.22108/ijgt.2013.2441ENMartynDixonUniversity
of AlabamaLeonidKurdachenkoNational University of DnepropetrovskJavierJavierUniversity of ZaragozaJournal Article20121016A celebrated result of I. Schur asserts that the derived subgroup of a group is finite provided the group modulo its center is finite, a result that has been the source of many investigations within the Theory of Groups. In this paper we exhibit a similar result to Schur's Theorem for vector spaces, acted upon by certain groups. The proof of this analogous result depends on the characteristic of the underlying field. We also give linear versions of corresponding theorems of R. Baer and P. Hall.https://ijgt.ui.ac.ir/article_2441_6e51a998a5edd8bad3956870b5f1843b.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76502120130301Certain combinatorial topics in group theory91107243910.22108/ijgt.2013.2439ENC.GuptaUniversity of ManitobaJournal Article20121211This article is intended to be a survey on some combinatorial topics in group theory. The bibliography at the end is neither claimed to be exhaustive, nor is it necessarily connected with a reference in the text. I include it as I see it revolves around the concepts which are discussed in the text.https://ijgt.ui.ac.ir/article_2439_e6c3c39c0bb1c0285110d472d9596943.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76502120130301On some invariants of finite groups109115264210.22108/ijgt.2013.2642ENJanKrempaInstitute of Mathematics, University of WarsawAgnieszkaStockaInstitute of Mathematics
University of BiałystokJournal Article20121218A normal subgroup $N$ of a group $G$ is said to be an <em>omissible</em> subgroup of $G$ if it has the following property: whenever $X\leq G$ is such that $G=XN$, then $G=X$. In this note we construct various groups $G$, each of which has an omissible subgroup $N\neq 1$ such that $G/N\cong SL_2(k)$ where $k$ is a field of positive characteristic.https://ijgt.ui.ac.ir/article_2642_9f742c032856a8f0dcd5a8b7de56b25b.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76502120130301Metahamiltonian groups and related topics117129267310.22108/ijgt.2013.2673ENMariaDe FalcoDipartimento di Matematica e Applicazioni - University of Napoli "Federico II"FrancescoDe GiovanniDipartimento di Matematica e Applicazioni - University of Napoli "Federico II"CarmelaMusellaDipartimento di Matematica e Applicazioni - University of Napoli "Federico II"Journal Article20121230A group $G$ is called <em>metahamiltonian</em> if all its non-abelian subgroups are normal. The aim of this paper is to provide an updated survey of research concerning certain classes of generalized metahamiltonian groups, in various contexts, and to prove some new results. Some open problems are listed.https://ijgt.ui.ac.ir/article_2673_d66ef73f5f08783c1a5e937dd4934f0c.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76502120130301Covering monolithic groups with proper subgroups131144267410.22108/ijgt.2013.2674ENMartinoGaronziUniversity of PadovaJournal Article20121230Given a finite non-cyclic group $G$, call $\sigma(G)$ the smallest number of proper subgroups of $G$ needed to cover $G$. Lucchini and Detomi conjectured that if a nonabelian group $G$ is such that $\sigma(G) < \sigma(G/N)$ for every non-trivial normal subgroup $N$ of $G$ then $G$ is <em>monolithic</em>, meaning that it admits a unique minimal normal subgroup. In this paper we show how this conjecture can be attacked by the direct study of monolithic groups.https://ijgt.ui.ac.ir/article_2674_ea33a8a83df38a9fbe3ccb5bf483e473.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76502120130301Omissible extensions of SL2(k) where k is a field of positive characteristic145155273910.22108/ijgt.2013.2739ENMartynDixonThe University of AlabamaMartinEvansThe University of AlabamaHowardSmithBucknell UniversityJournal Article20121219A normal subgroup $N$ of a group $G$ is said to be an <em>omissible</em> subgroup of $G$ if it has the following property: whenever $X\leq G$ is such that $G=XN$, then $G=X$. In this note we construct various groups $G$, each of which has an omissible subgroup $N\neq 1$ such that $G/N\cong SL_2(k)$ where $k$ is a field of positive characteristic.https://ijgt.ui.ac.ir/article_2739_5cbd1f85252078e642252fe7f93e9285.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76502120130301Supersoluble conditions and transfer control157166274010.22108/ijgt.2013.2740ENAnna LuisaGilottiUniversita BolognaLuigiSerenaDipartimento di Matematica U. Dini
Viale Morgagni 67/A
50134 FIRENZEJournal Article20120627In this paper we give a new condition for a Sylow $p$-subgroup of a finite group to control transfer. Then it is deduced a characteri-zation of supersoluble groups that can be seen as a generalization of the well known result concerning the supersolubility of finite groups with cyclic Sylow subgroups. Moreover a condition for a normal embedding of a strongly closed $p$-subgroup is given. These results make use of the properties of $G$-chains and $\Phi$-chains.<br /> https://ijgt.ui.ac.ir/article_2740_448422e5d677e318f74f297e7784d5a0.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76502120130301A finiteness condition on the coefficients of the probabilistic zeta function167174276010.22108/ijgt.2013.2760ENHoang DungDuongMathematisch Instituut, Leiden Universiteit, Niels Bohrweg 1, 2333 CA Leiden, The NetherlandsAndreaLucchiniDipartimento di Matematica
Università di PadovaJournal Article20121222We discuss whether finiteness properties of a profinite group $G$ can be deduced from the coefficients of the probabilistic zeta function $P_G(s)$. In particular we prove that if $P_G(s)$ is rational and all but finitely many non abelian composition factors of $G$ are isomorphic to $PSL(2,p)$ for some prime $p$, then $G$ contains only finitely many maximal subgroups.https://ijgt.ui.ac.ir/article_2760_6ca06204ff8803a9692e43ba9bbb64d6.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76502120130301The prime graph conjecture for integral group rings of some alternating groups175185275910.22108/ijgt.2013.2759ENMohamedSalimUNITED ARAB EMIRATES UNIVERSITYJournal Article20130322We investigate the classical H. Zassenhaus conjecture for integral group rings of alternating groups $A_9$ and $A_{10}$ of degree $9$ and $10$, respectively. As a consequence of our previous results we confirm the Prime Graph Conjecture for integral group rings of $A_n$ for all $n \leq 10$.https://ijgt.ui.ac.ir/article_2759_c14fa9a571a2516ee5a9f8892f18fddc.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76502120130301On the representation theory of the alternating groups187198284110.22108/ijgt.2013.2841ENTullioCeccherini-SilbersteinDipartimento di Ingegneria, Università del SannioFabioScarabottiDipartimento SBAI, Sapienza Universita' di RomaFilippoTolliDipartimento di Matematica e Fisica, Universita' Roma TreJournal Article20130114We present the basic results on the representation theory of the alternating groups $A_n$. Our approach is based on Clifford theory.https://ijgt.ui.ac.ir/article_2841_21712515b0e5f7db680433e0809ea2ed.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76502120130301On finite arithmetic groups199227286510.22108/ijgt.2013.2865ENDmitryMalininI.H.E.S.Journal Article20121227Let $F$ be a finite extension of $\Bbb Q$, ${\Bbb Q}_p$ or a global field of positive characteristic, and let $E/F$ be a Galois extension. We study the realization fields of finite subgroups $G$ of $GL_n(E)$ stable under the natural operation of the Galois group of $E/F$. Though for sufficiently large $n$ and a fixed algebraic number field $F$ every its finite extension $E$ is realizable via adjoining to $F$ the entries of all matrices $g\in G$ for some finite Galois stable subgroup $G$ of $GL_n(\Bbb C)$, there is only a finite number of possible realization field extensions of $F$ if $G\subset GL_n(O_E)$ over the ring $O_E$ of integers of $E$. After an exposition of earlier results we give their refinements for the realization fields $E/F$. We consider some applications to quadratic lattices, arithmetic algebraic geometry and Galois cohomology of related arithmetic groups.https://ijgt.ui.ac.ir/article_2865_15eedcf8206252b2004de346b12153d2.pdf