University of IsfahanInternational Journal of Group Theory2251-76507120180301Proceedings of Ischia Group Theory 20162452310.22108/ijgt.2018.24523ENJournal Article20200311https://ijgt.ui.ac.ir/article_24523_b70e0c7a81ee270daea0fefc923e6716.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76507120180301On groups with a restriction on normal subgroups142123710.22108/ijgt.2016.21237ENAlessioRussoSeconda Universita di Napoli0000-0002-5336-0347Journal Article20160630The structure of infinite groups in which every (proper) normal subgroup is the only one of its cardinality is investigated in the universe of groups without infinite simple sections. The corrisponding problem for finite soluble groups was considered by M. Curzio (1958).https://ijgt.ui.ac.ir/article_21237_404c5b3acc80442c0389dbab78844bf3.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76507120180301Countably recognizable classes of groups with restricted conjugacy classes5162123510.22108/ijgt.2016.21235ENFrancescoDe GiovanniDipartimento di Matematica e Applicazioni - University of Napoli &quot;Federico II&quot;MarcoTrombettiUniversita di Napoli Federico II,0000-0003-4532-3690Journal Article20160430A group class ${ X}$ is said to be countably recognizable if a group belongs to ${X}$ whenever all its countable subgroups lie in ${X}$. It is proved here that most of the relevant classes of groups defined by restrictions on the conjugacy classes are countably recognizable.https://ijgt.ui.ac.ir/article_21235_894f1a96aa9ff81f3b1db138105bf512.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76507120180301Detecting the prime divisors of the character degrees and the class sizes by a subgroup generated with few elements17212122010.22108/ijgt.2017.21220ENAndreaLucchiniDipartimento di Matematica
Università di Padova0000-0002-2134-4991Journal Article20160718We prove that every finite group $G$ contains a three-generated subgroup $H$ with the following property: a prime $p$ divides the degree of an irreducible character of $G$ if and only if it divides the degree of an irreducible character of $H.$ There is no analogous result for the prime divisors of the sizes of the conjugacy classes.https://ijgt.ui.ac.ir/article_21220_7d6849ef0c0f20d2874ee36c05cf3ef1.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76507120180301Conjugacy classes contained in normal subgroups: an overview23362121610.22108/ijgt.2017.21216ENAntonioBeltranUniversitat Jaume IMariaJose FelipeUniversitat Politécnica de ValènciaCarmenMelchorUniversitat Jaume IJournal Article20161013We survey known results concerning how the conjugacy classes contained in a normal subgroup and their sizes exert an influence on the normal structure of a finite group. The approach is mainly presented in the framework of graphs associated to the conjugacy classes, which have been introduced and developed in the past few years. We will see how the properties of these graphs, along with some extensions of the classic Landau's Theorem on conjugacy classes for normal subgroups, have been used in order to classify groups and normal subgroups satisfying certain conjugacy class numerical conditions.https://ijgt.ui.ac.ir/article_21216_521a00edf9dcb7b91295b2b081a9a468.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76507120180301On the relationships between the factors of the upper and lower central series in some non-periodic groups37502167410.22108/ijgt.2017.21674ENMartynDixonUniversity of AlabamaLeonidKurdachenkoNational University of DnepropetrovskIgorSubbotinNational UniversityJournal Article20160914This paper deals with the mutual relationships between the factor group $G/zeta(G)$ (respectively $G/zeta_k(G)$) and $G'$ (respectively $gamma_{k+1}(G)$ and $G^{mathfrak{N}}$). It is proved that if $G/zeta(G)$ (respectively $G/zeta_k(G)$) has finite $0$-rank, then $G'$ (respectively $gamma_{k+1}(G)$ and $G^{mathfrak{N}}$) also have finite $0$-rank. Furthermore, bounds for the $0$-ranks of $G', gamma_{k+1}(G)$ and $G^{mathfrak{N}}$ are obtained.https://ijgt.ui.ac.ir/article_21674_99f61bdccf031d8e387d46fc8009fb86.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76507120180301Regular subgroups, nilpotent algebras and projectively congruent matrices51562121510.22108/ijgt.2017.21215ENMarcoPellegriniUniversit&agrave; Cattolica del Sacro CuoreJournal Article20161018In this paper we highlight the connection between certain classes of regular subgroups of the affine group $AGL_n(F)$, $F$ a field, and associative nilpotent $F$-algebras of dimension $n$. We also describe how the classification of projective congruence classes of square matrices is equivalent to the classification of regular subgroups of particular shape.https://ijgt.ui.ac.ir/article_21215_2ad48b9247fe4edac37cbe792dfa993c.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76507120180301On groups with two isomorphism classes of central factors57642121810.22108/ijgt.2016.21218ENSerenaSianiUniversitamp;agrave; degli Studi di SalernoJournal Article20160824The structure of groups which have at most two isomorphism classes of central factors ($B_2$-groups) are investigated. A complete description of $B_2$-groups is obtained in the locally finite case and in the nilpotent case. In addition detailed information is obtained about soluble $B_2$-groups. Also structural information about insoluble $B_2$-groups is given, in particular when such a group has the derived subgroup satisfying the minimal condition.https://ijgt.ui.ac.ir/article_21218_ce8d518bf9ab00038546f615ced4d6d7.pdf