Name: Statistically characterized subgroups related to some non-arithmetic sequence of integers
Keywords: natural density, Density, gaps, topology, General Topology (math.GN), General properties and structure of LCA groups, Group Theory (math.GR), characterized subgroup, $s$-characterized subgroup, arithmetic sequence, Convergence and divergence of series and sequences, circle group

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 May 2025Embargo end date: 01 Jan 2024 English Publisher:Elsevier BVJournal:Expositiones Mathematicae, volume 43, page 125,653 (issn: 0723-0869,

Authors: Pratulananda Das; Ayan Ghosh;

doi: 10.1016/j.exmath.2025.125653 , 10.48550/arxiv.2404.15905

arXiv: 2404.15905

Statistically characterized subgroups related to some non-arithmetic sequence of integers

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Abstract

Recently, in Das et al. (Mediterr. J. Math. 21 : 164, 2024), characterized subgroups are investigated for some special kind of non-arithmetic sequences. In this note, we study subsequent problems in case of ``statistically characterized subgroups" introduced in Dikranjan et al. (Fund. Math. 249 : 185-209, 2020). The entire investigation emphasizes that these statistically characterized subgroups are mostly larger in size, having cardinality $\mathfrak{c}$, and exhibit behavior that significantly differs from that of classically characterized subgroups. As a consequence, we solve an open problem raised in Dikranjan et al. (Fund. Math. 249 : 185-209, 2020).

Keywords

natural density, Density, gaps, topology, General Topology (math.GN), General properties and structure of LCA groups, Group Theory (math.GR), characterized subgroup, $s$-characterized subgroup, arithmetic sequence, Convergence and divergence of series and sequences, circle group, FOS: Mathematics, statistical convergence, Mathematics - Group Theory, Mathematics - General Topology

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