University of IsfahanInternational Journal of Group Theory2251-76509120200301Proceedings of the Ischia Group Theory 20182452010.22108/ijgt.2020.24520ENJournal Article20200309https://ijgt.ui.ac.ir/article_24520_49442d925c6ec5383da7bfaeb463667d.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76509120200301A probabilistic version of a theorem of László Kovács and Hyo-Seob Sim162307310.22108/ijgt.2018.112531.1496ENAndreaLucchiniDipartimento di Matematica
Università di PadovaMariapiaMoscatielloDipartimento di Matematica Università di PadovaJournal Article20180814For a finite group group, denote by $\mathcal V(G)$ the smallest positive integer $k$ with the property that the probability of generating $G$ by $k$ randomly chosen elements is at least $1/e.$ Let $G$ be a finite soluble group. {Assume} that for every $p\in \pi(G)$ there exists $G_p\leq G$ such that $p$ does not divide $|G:G_p|$ and ${\mathcal V}(G_p)\leq d.$ Then ${\mathcal V}(G)\leq d+7.$https://ijgt.ui.ac.ir/article_23073_26232b99d2d66bbcad0f18ccab2e0578.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76509120200301On some generalization of the malnormal subgroups7242312610.22108/ijgt.2018.112124.1487ENLeonid AKurdachenkoNational University of DniproNikolaiSemkoUniversity of State Fiscal Service of UkraineIgorSubbotinDepartment of Mathematics and Natural Sciences, College of Letters and Sciences,
National University, USAJournal Article20180717A subgroup $H$ of a group $G$ is called malonormal in $G$ if $H \cap H^x =\langle 1\rangle$ for every element $x \notin N_G(H)$. These subgroups are generalizations of malnormal subgroups. Every malnormal subgroup is malonormal, and every selfnormalizing malonormal subgroup is malnormal. Furthermore, every normal subgroup is malonormal. In this paper we obtain a description of finite and certain infinite groups, whose subgroups are malonormal.https://ijgt.ui.ac.ir/article_23126_688dc34354e02beddf76d33a8c23e1d0.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76509120200301$4$-Quasinormal subgroups of prime order25302312710.22108/ijgt.2018.113482.1510ENStewart EdwardStonehewerUniversity of WarwickJournal Article20181017Generalizing the concept of quasinormality, a subgroup $H$ of a group $G$ is said to be 4-quasinormal in $G$ if, for all cyclic subgroups $K$ of $G$, $\langle H,K\rangle=HKHK$. An intermediate concept would be 3-quasinormality, but in finite $p$-groups - our main concern - this is equivalent to quasinormality. Quasinormal subgroups have many interesting properties and it has been shown that some of them can be extended to 4-quasinormal subgroups, particularly in finite $p$-groups. However, even in the smallest case, when $H$ is a 4-quasinormal subgroup of order $p$ in a finite $p$-group $G$, precisely how $H$ is embedded in $G$ is not immediately obvious. Here we consider one of these questions regarding the commutator subgroup $[H,G]$.https://ijgt.ui.ac.ir/article_23127_e1941b7ccb2a1ff74d7c8eb583763bbe.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76509120200301The number of maximal subgroups and probabilistic generation of finite groups31422326010.22108/ijgt.2019.114469.1521ENAdolfoBallester BolinchesDepartament de Matematiques, Universitat de Valencia, SpainRamónEsteban-RomeroDepartament de Matematiques, Universitat de Valencia, SpainPazJiménez-SeralDepartamento de Matematicas, Universidad de Zaragoza, Pedro Cerbuna, SpainHangyangMengDepartament de Matematiques, Universitat de Valencia, SpainJournal Article20181210In this survey we present some significant bounds for the number of maximal subgroups of a given index of a finite group. As a consequence, new bounds for the number of random generators needed to generate a finite $d$-generated group with high probability which are significantly tighter than the ones obtained in the paper of Jaikin-Zapirain and Pyber (Random generation of finite and profinite groups and group enumeration, \emph{Ann.\ Math.}, \textbf{183} (2011) 769--814) are obtained. The results of Jaikin-Zapirain and Pyber, as well as other results of Lubotzky, Detomi, and Lucchini, appear as particular cases of our theorems.https://ijgt.ui.ac.ir/article_23260_a1e34939c5076bd89068d8b7b5d04b45.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76509120200301Groups with many self-centralizing or self-normalizing subgroups43572327710.22108/ijgt.2019.114315.1518ENCostantinoDeliziaDepartment of Mathematics, University of Salerno, ItalyChiaraNicoteraDepartment of Mathematics, University of Salerno, ItalyJournal Article20181202The purpose of this paper is to present a comprehensive overview of known and new results concerning the structure of groups in which all subgroups, except those having a given property, are either self-centralizing or self-normalizing.https://ijgt.ui.ac.ir/article_23277_e98b5cfe19105e4c00b179320052e0aa.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76509120200301Some problems about products of conjugacy classes in finite groups59682343410.22108/ijgt.2019.111448.1480ENAntonioBeltránDepartamento de Matematicas, Universidad Jaume I, 12071, Castellon, SpainMaría JoséFelipeInstituto Universitario de Matematica Pura y Aplicada, Universitat Politecnica de Valencia, 46022, Valencia, SpainCarmenMelchorDepartamento de Matematicas, Universidad Jaume I, 12071, Castellon, SpainJournal Article20180606We summarize several results about non-simplicity, solvability and normal structure of finite groups related to the number of conjugacy classes appearing in the product or the power of conjugacy classes. We also collect some problems that have only been partially solved.https://ijgt.ui.ac.ir/article_23434_743d3a0de35dd083ec6f3a8658a13b57.pdf