{"title":"阿贝尔群的循环子群传递性","authors":"B. Goldsmith, K. Gong, L. Strüngmann","doi":"10.4171/rsmup/143","DOIUrl":null,"url":null,"abstract":". In previous work the (cid:12)rst two authors studied the notion of transitivity with respect to cyclic subgroups for separable Abelian p -groups and modules over the ring of p -adic integers. Here we consider brie(cid:13)y how the notion can be used in the context of torsion-free Abelian groups and also look at the situation for non-separable p -groups and direct sums of in(cid:12)nite rank homocyclic p -groups.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"53 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Cyclic subgroup transitivity for Abelian groups\",\"authors\":\"B. Goldsmith, K. Gong, L. Strüngmann\",\"doi\":\"10.4171/rsmup/143\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". In previous work the (cid:12)rst two authors studied the notion of transitivity with respect to cyclic subgroups for separable Abelian p -groups and modules over the ring of p -adic integers. Here we consider brie(cid:13)y how the notion can be used in the context of torsion-free Abelian groups and also look at the situation for non-separable p -groups and direct sums of in(cid:12)nite rank homocyclic p -groups.\",\"PeriodicalId\":20997,\"journal\":{\"name\":\"Rendiconti del Seminario Matematico della Università di Padova\",\"volume\":\"53 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-12-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Rendiconti del Seminario Matematico della Università di Padova\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/rsmup/143\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Rendiconti del Seminario Matematico della Università di Padova","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/rsmup/143","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
. In previous work the (cid:12)rst two authors studied the notion of transitivity with respect to cyclic subgroups for separable Abelian p -groups and modules over the ring of p -adic integers. Here we consider brie(cid:13)y how the notion can be used in the context of torsion-free Abelian groups and also look at the situation for non-separable p -groups and direct sums of in(cid:12)nite rank homocyclic p -groups.
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