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arXiv · 2404.15905

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

Pratulananda Das·Ayan Ghosh
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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).

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Pratulananda Das, Ayan Ghosh. 2024-04-24. Statistically characterized subgroups related to some non-arithmetic sequence of integers. https://arxiv.org/abs/2404.15905

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