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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Pages 55-66Graph 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
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Pages 67-80In 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
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Pages 81-98In 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
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Pages 99-109The 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
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Pages 111-121This 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