{"title":"Statistically characterized subgroups related to some non-arithmetic sequence of integers","authors":"Pratulananda Das, Ayan Ghosh","doi":"10.1016/j.exmath.2025.125653","DOIUrl":null,"url":null,"abstract":"<div><div>Very recently in Das and Ghosh (2024), characterized subgroups have been investigated for some special kind of non-arithmetic sequences where certain cardinality related questions were answered. As statistically characterized subgroups Dikranjan et al. (2020) have evolved as non-trivial generalization of characterized subgroups, it is natural to ask the same questions for these subgroups which we try to answer here. The entire investigation emphasizes that these statistically characterized subgroups are mostly larger in size, having cardinality <span><math><mi>c</mi></math></span>, and exhibit behavior that significantly differs from that of classical characterized subgroups. As a consequence, we are able to present solution of an open problem raised in Dikranjan et al. (2020).</div></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"43 3","pages":"Article 125653"},"PeriodicalIF":0.8000,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Expositiones Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0723086925000088","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
Very recently in Das and Ghosh (2024), characterized subgroups have been investigated for some special kind of non-arithmetic sequences where certain cardinality related questions were answered. As statistically characterized subgroups Dikranjan et al. (2020) have evolved as non-trivial generalization of characterized subgroups, it is natural to ask the same questions for these subgroups which we try to answer here. The entire investigation emphasizes that these statistically characterized subgroups are mostly larger in size, having cardinality , and exhibit behavior that significantly differs from that of classical characterized subgroups. As a consequence, we are able to present solution of an open problem raised in Dikranjan et al. (2020).
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