J. T. Otobong, Eno John, M. U. Udeme, Michael N. John
{"title":"Ulm Function Analysis of Full Transitivity in Primary Abelian Groups","authors":"J. T. Otobong, Eno John, M. U. Udeme, Michael N. John","doi":"10.37745/ijmss.13/vol12n118","DOIUrl":null,"url":null,"abstract":"This research addresses the problem posed by Chekhlov and Danchev (2015) regarding variations of Kaplansky's full transitivity in primary abelian groups 𝐺. By delving into three distinct forms of full transitivity within the endomorphism ring of 𝐺, specifically focusing on subgroups, subrings, and unitary subrings generated by commutator endomorphisms, we aim to provide a comprehensive understanding of the totally projective groups exhibiting these properties. The Ulm function of 𝐺 emerges as a key tool in solving this problem and related inquiries, leading to a precise characterization of the groups involved.","PeriodicalId":476297,"journal":{"name":"International journal of mathematics and statistics studies","volume":"345 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International journal of mathematics and statistics studies","FirstCategoryId":"0","ListUrlMain":"https://doi.org/10.37745/ijmss.13/vol12n118","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
This research addresses the problem posed by Chekhlov and Danchev (2015) regarding variations of Kaplansky's full transitivity in primary abelian groups 𝐺. By delving into three distinct forms of full transitivity within the endomorphism ring of 𝐺, specifically focusing on subgroups, subrings, and unitary subrings generated by commutator endomorphisms, we aim to provide a comprehensive understanding of the totally projective groups exhibiting these properties. The Ulm function of 𝐺 emerges as a key tool in solving this problem and related inquiries, leading to a precise characterization of the groups involved.
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