فهرست مطالب

International Journal of Group Theory
Volume:9 Issue: 2, Jun 2020

  • تاریخ انتشار: 1398/12/28
  • تعداد عناوین: 7
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  • Proceedings of Ischia Group Theory 2018
    Alireza Abdollahi Page 1
    View Paper Editorial Original: English
  • Catalan fragile words
    Daniele D´Angeli, Alfredo Donno *, Emanuele Rodaro Pages 69-80
    ‎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.
    Keywords: Automata group, Catalan number, Fragile word, Full binary tree
    Abstract View Paper Research/Original Article Original: English
  • Topological loops with solvable multiplication groups of dimension at most six are centrally nilpotent
    Agota Figula *, Ameer Al Abayechi Pages 81-94

    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.

    Keywords: Multiplication group, inner mapping group of topological loops, topological transformation group, solvable Lie algebras, centrally nilpotent loops
    Abstract View Paper Research/Original Article Original: English
  • Groups with numerical restrictions ‎on minimal generating sets
    Leonid Kurdachenko, Patrizia Longobardi, Mercede Maj * Pages 95-111
    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 $S^2 leq 3|S|-beta$, where $beta in {1, 2, 3}$
    Keywords: Small doubling, minimal generating subsets, inverse problems
    Abstract View Paper Research/Original Article Original: English
  • A survey on groups with some restrictions on normalizers or centralizers
    Leire Legarreta *, Maria Tota Pages 113-124
    We consider conditions on normalizers or centralizers in a group and we collect results showing how such conditions influence the structure of the group.
    Keywords: Centralizers, normalizers, finite p-groups, locally finite groups, locally nilpotent groups
    Abstract View Paper Research/Original Article Original: English
  • Open normal subgroups in normally constrained pro-p groups
    Norberto Gavioli, Leire Legarreta *, Marco Ruscitti, Carlo Maria Scoppola Pages 125-132

    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.

    Keywords: ‎pro-‎‎p‎ groups‎, ‎open (closed) normal subgroups‎, ‎waist‎, ‎width‎, ‎powerful
    Abstract View Paper Research/Original Article Original: English
  • Integral forms in vertex operator algebras, a survey
    Robert Griess * Pages 133-138
    We give a brief survey of recent work on integral forms in vertex operator algebras (VOAs).
    Keywords: integral forms, vertex algebra, vertex operator algebra, Finite group, invariant
    Abstract View Paper Research/Original Article Original: English