University of Isfahan International Journal of Group Theory 2251-7650 9 2 2020 06 01 Catalan fragile words 69 80 23435 10.22108/ijgt.2019.113180.1506 EN Daniele D'Angeli TUGraz Alfredo Donno Università degli Studi Niccolò Cusano Dipartimento di Ingegneria Via Don Carlo Gnocchi, 3 00166 Roma, Italy Emanuele Rodaro Dipartimento di Matematica, Politecnico di Milano, Milano, Italia Journal Article 2018 10 03 ‎Fragile words have been already considered in the context of automata groups‎. ‎Here we focus our attention on a special class of strongly fragile words that we call Catalan fragile words‎. ‎Among other properties‎, ‎we show that there exists a one-to-one correspondence between the set of Catalan fragile words and the set of full binary trees‎. Automata group Catalan number Fragile word Full binary tree https://ijgt.ui.ac.ir/article_23435_55a44b9deabef92baa68e39860e518aa.pdf
University of Isfahan International Journal of Group Theory 2251-7650 9 2 2020 06 01 Topological loops with solvable multiplication groups of dimension at most six are centrally nilpotent 81 94 23511 10.22108/ijgt.2019.114770.1522 EN Agota Figula Institute of Mathematics, University of Debrecen, Debrecen, Hungary Ameer Al-Abayechi Institute of Mathematics, University of Debrecen, Debrecen, Hungary Journal Article 2018 12 28 The main result of our consideration is the proof of the centrally nilpotency of class two property for connected topological proper loops $L$ of dimension $\le 3$ which have an at most six-dimensional solvable indecomposable Lie group as their multiplication group. This theorem is obtained from our previous classification by the investigation of six-dimensional indecomposable solvable multiplication Lie groups having a five-dimensional nilradical. We determine the Lie algebras of these multiplication groups and the subalgebras of the corresponding inner mapping groups. Multiplication group and inner mapping group of topological loops topological transformation group solvable Lie algebras centrally nilpotent loops https://ijgt.ui.ac.ir/article_23511_9f0b68dcbecfb72da78de4a261cbfbd0.pdf
University of Isfahan International Journal of Group Theory 2251-7650 9 2 2020 06 01 Groups with numerical restrictions ‎on minimal generating sets 95 111 23278 10.22108/ijgt.2019.115131.1526 EN Leonid A Kurdachenko National University of Dnipro Patrizia Longobardi Dipartimento di Matematica Universita' di Salerno Mercede Maj University of Salerno Journal Article 2019 01 15 We study an inverse problem of small doubling type. We investigate the structure of a finitely generated group $G$ such that, for any set $S$ of generators of $G$ of minimal order, we have $S^2 ≤ 3|S|-ß$, where $ß ∈ {1, 2, 3}$ Small doubling minimal generating subsets inverse problems https://ijgt.ui.ac.ir/article_23278_6bdfc95183f7f344bc57892a5e13ac7a.pdf
University of Isfahan International Journal of Group Theory 2251-7650 9 2 2020 06 01 A survey on groups with some restrictions on normalizers or centralizers 113 124 23436 10.22108/ijgt.2019.115244.1529 EN Leire Legarreta Department of Mathematics, University of the Basque Country, Spain Maria Tota Departament of Mathematics, University of Salerno, Italy Journal Article 2019 01 22 We consider conditions on normalizers or centralizers in a group and we collect results showing how such conditions influence the structure of the group. Centralizers normalizers finite p-groups locally finite groups locally nilpotent groups https://ijgt.ui.ac.ir/article_23436_4dc95657c63d6db3c66115d229638ec8.pdf
University of Isfahan International Journal of Group Theory 2251-7650 9 2 2020 06 01 Open normal subgroups in normally constrained pro-$p$ groups 125 132 23588 10.22108/ijgt.2019.115382.1532 EN Norberto Gavioli Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica, Università degli studi dell'Aquila Leire Legarreta Spanish Marco Ruscitti Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica, Università degli studi dell'Aquila Carlo Maria Scoppola Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica, Università degli studi dell'Aquila Journal Article 2019 01 30 In this paper we analyse properties satisfied by certain open normal subgroups in normally constrained pro-‎$‎p‎$ groups and in a spread version of normally constrained pro-‎$‎p‎$‎ groups‎. ‎In the case of powerful normally constrained pro-‎$‎p‎$ groups‎, ‎we exhibit some kind of inheritance properties in certain open normal subgroups‎. ‎pro-‎$‎p‎$ groups‎ ‎open (closed) normal subgroups‎ ‎waist‎ ‎width‎ ‎powerful https://ijgt.ui.ac.ir/article_23588_b6a90fc98eb0f50b87dc9c8f3918a26d.pdf
University of Isfahan International Journal of Group Theory 2251-7650 9 2 2020 06 01 Integral forms in vertex operator algebras, a survey 133 138 24361 10.22108/ijgt.2020.114954.1523 EN Robert L. Griess University of Michigan Journal Article 2019 01 07 We give a brief survey of recent work on integral forms in vertex operator algebras (VOAs). integral forms vertex algebra vertex operator algebra Finite group invariant https://ijgt.ui.ac.ir/article_24361_367d35051e12999b562208c6b31555ad.pdf