University of IsfahanInternational Journal of Group Theory2251-76509320200901Finite groups with seminormal or abnormal Sylow subgroups1391422321310.22108/ijgt.2018.112602.1500ENVictor StepanovichMonakhovFrancisk Skorina Gomel State University, Department of Mathematics, Sovetskaya str., 104, Gomel, 246019,
Republic of BelarusIrinaSokhorPhysic and Mathematic Department, Brest State A.S. Pushkin University, Brest, BelarusJournal Article20180819Let $G$ be a finite group in which every Sylow subgroup is seminormal or abnormal. We prove that $G$ has a Sylow tower. We establish that if a group has a maximal subgroup with Sylow subgroups under the same conditions, then this group is soluble.http://ijgt.ui.ac.ir/article_23213_e264600201db5f1c28650722665fff42.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76509320200901Faithful real representations of groups of $F$-type1431552375510.22108/ijgt.2018.112439.1494ENBenjaminFineDepartment of Mathematics
Fairfield Universiry
Fairfield, CT 06840AnjaMoldenhauerDepartment of Mathematics
University of HamburgGerhardRosnebergerDepartment of Mathematics
University of HmaburgJournal Article20170330Groups of $F$-type were introduced in [B. Fine and G. Rosenberger, Generalizing Algebraic Properties of Fuchsian Groups, emph{London Math. Soc. Lecture Note Ser.}, textbf{159} (1991) 124--147.] as a natural algebraic generalization of Fuchsian groups. They can be considered as the analogs of cyclically pinched one-relator groups where torsion is allowed. Using the methods In [B. Fine. M. Kreuzer and G. Rosenberger, Faithful Real Representations of Cyclically Pinched One-Relator Groups, <em>Int. J. Group Theory</em>, <strong>3</strong> (2014) 1--8.] we prove that any hyperbolic group of $F$-type has a faithful representation in $PSL(2,mathbb R)$. From this we also obtain that a cyclically pinched one-relator group has a faithful real representation if and only if it is hyperbolic. We further survey the many nice properties of groups of $F$-type. http://ijgt.ui.ac.ir/article_23755_2af5ed775b029833bc7eff5c527aaaeb.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76509320200901Minimal embeddings of small finite groups1571832403410.22108/ijgt.2019.112560.1497ENRobertHeffernanDepartment of Mathematics,
Cork Institute of Technology,
Bishopstown,
Cork,
Ireland.BrendanMcCannDepartment of Computing and Mathematics, Waterford Institute of Technology, Waterford, IrelandJournal Article20180816We determine the groups of minimal order in which all groups of order $n$ can embedded for $ 1 le n le 15$. We further determine the minimal order of a group in which all groups of order $n$ or less can be embedded, also for $ 1 le n le 15$.http://ijgt.ui.ac.ir/article_24034_7e93a27438d4099810093b2c0743fc9c.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76509320200901Omegas of agemos in powerful groups1851922347810.22108/ijgt.2019.113217.1507ENJamesWilliamsDepartment of Mathematical Sciences, University of Bath, UKJournal Article20181005In this note we show that for any powerful $p$-group $G$, the subgroup $Omega_{i}(G^{p^{j}})$ is powerfully nilpotent for all $i,jgeq1$ when $p$ is an odd prime, and $igeq1$, $jgeq2$ when $p=2$. We provide an example to show why this modification is needed in the case $p=2$. Furthermore we obtain a bound on the powerful nilpotency class of $Omega_{i}(G^{p^{j}})$.http://ijgt.ui.ac.ir/article_23478_810f62ccfd0e1bd777c04927c851b273.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76509320200901$4$-Regular prime graphs of nonsolvable groups1932222371810.22108/ijgt.2019.112277.1490ENDonnieKasyokiSchool of Mathematics, Statistics and Actuarial Science, Maseno University,
KenyaPaulOlecheDepartment of Pure and Mathematics, Maseno University, P.O. Box 333, Maseno, KenyaJournal Article20180727Let $G$ be a finite group and $cd(G)$ denote the character degree set for $G$. The prime graph $DG$ is a simple graph whose vertex set consists of prime divisors of elements in $cd(G)$, denoted $rho(G)$. Two primes $p,qin rho(G)$ are adjacent in $DG$ if and only if $pq|a$ for some $ain cd(G)$. We determine which simple 4-regular graphs occur as prime graphs for some finite nonsolvable group.http://ijgt.ui.ac.ir/article_23718_69ca905b94960ef358bf148a4b31e12a.pdf