فهرست مطالب

International Journal of Group Theory
Volume:12 Issue: 2, Jun 2023

  • تاریخ انتشار: 1401/10/06
  • تعداد عناوین: 5
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  • Gelfand pairs associated with the action of graph automaton groups
    Matteo Cavaleri, Daniele D’Angeli, Alfredo Donno * Pages 55-66
    Graph automaton groups constitute a special class of automaton groups constructed from a graph. In this paper, we show that the action of any graph automaton group on each level of the rooted regular tree gives rise to a Gelfand pair. In particular, we determine the irreducible submodules of the action of such a group on the space of functions defined on each level of the tree, and we exhibit the corresponding spherical functions.
    Keywords: Graph automaton group, Gelfand pair, Rooted regular tree, $2$-points homogeneous action, Spherical function
    Abstract View Paper Research/Original Article Original: English
  • Isometry groups of six-dimensional filiform nilmanifolds
    Agota Figula *, Sameer Annon Abbas Pages 67-80
    In this paper, we classify up to isometry the connected and simply connected Riemannian nilmanifolds on six-dimensional filiform Lie groups and we compute the corresponding isometry groups.
    Keywords: filiform nilpotent Lie groups, filiform metric Lie algebras, isometry groups of nilmanifolds, the group of orthogonal automorphisms of metric Lie algebras
    Abstract View Paper Research/Original Article Original: English
  • On pairs of antagonistic subgroups and theirs influence on the structure of groups
    Leonid Kurdachenko, Patrizia Longobardi, Mercede Maj *, Javier Otal Pages 81-98
    In this survey we collect some results on the influence on the structure of a group of some families of its subgroups satisfying conditions related to normality. In particular we focus on groups whose subgroups have two antagonistic properties.
    Keywords: normal, subnormal, ascendant, descendant, selfnormalizing, abnormal, conormal, contranormal, pronormal subgroups
    Abstract View Paper Research/Original Article Original: English
  • Some group-theoretical approaches to skew left braces
    Adolfo Ballester Bolinches, Ramon Esteban-Romero *, Paz Jiménez-Seral, Vicent Pérez-Calabuig Pages 99-109
    The algebraic structure of skew left brace has become a useful tool to construct set-theoretic solutions of the Yang-Baxter equation. In this survey we present some descriptions of skew left braces in terms of bijective derivations, triply factorised groups, and regular subgroups of the holomorph of a group, as well as some applications of these descriptions to the study of substructures, nilpotency, and factorised skew left braces.
    Keywords: Skew left brace, triply factorised group, Derivation, regular subgroup, nilpotency
    Abstract View Paper Research/Original Article Original: English
  • Advances on a construction related to the non-abelian tensor square of a group
    Raimundo Bastos, Carmine Monetta * Pages 111-121
    This is a survey on a group construction in connection with the non-abelian tensor square of groups. We report on the developments obtained in the last decade emphasizing the results from a commutator point of view.
    Keywords: structure theorems, finiteness conditions, exponent
    Abstract View Paper Research/Original Article Original: English