Products of locally cyclic groups
dc.contributor.author | Amberg, Bernhard | |
dc.contributor.author | Sysak, Yaroslav | |
dc.date.accessioned | 2022-07-04T08:32:42Z | |
dc.date.available | 2022-07-04T08:32:42Z | |
dc.date.issued | 2021 | |
dc.description.abstract | We consider groups of the form G=AB with two locally cyclic subgroups A and B. The structure of these groups is determined in the cases when A and B are both periodic or when one of them is periodic and the other is not. Together with a previous study of the case where A and B are torsion-free, this gives a complete classification of all groups that are the product of two locally cyclic subgroups. As an application, it is shown that the Prüfer rank of a periodic product of two locally cyclic subgroups does not exceed 3, and this bound is sharp. It is also proved that a product of a finite number of pairwise permutable periodic locally cyclic subgroups is a locally supersoluble group. This generalizes a well-known theorem of B. Huppert for finite groups. | en_GB |
dc.identifier.doi | http://doi.org/10.25358/openscience-7289 | |
dc.identifier.uri | https://openscience.ub.uni-mainz.de/handle/20.500.12030/7303 | |
dc.language.iso | eng | de |
dc.rights | CC-BY-4.0 | * |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | * |
dc.subject.ddc | 510 Mathematik | de_DE |
dc.subject.ddc | 510 Mathematics | en_GB |
dc.title | Products of locally cyclic groups | en_GB |
dc.type | Zeitschriftenaufsatz | de |
jgu.journal.title | Archiv der Mathematik | de |
jgu.journal.volume | 117 | de |
jgu.organisation.department | FB 08 Physik, Mathematik u. Informatik | de |
jgu.organisation.name | Johannes Gutenberg-Universität Mainz | |
jgu.organisation.number | 7940 | |
jgu.organisation.place | Mainz | |
jgu.organisation.ror | https://ror.org/023b0x485 | |
jgu.pages.end | 28 | de |
jgu.pages.start | 19 | de |
jgu.publisher.doi | 10.1007/s00013-021-01593-1 | de |
jgu.publisher.issn | 1420-8938 | de |
jgu.publisher.name | Springer | de |
jgu.publisher.place | Berlin u.a. | de |
jgu.publisher.year | 2021 | |
jgu.rights.accessrights | openAccess | |
jgu.subject.ddccode | 510 | de |
jgu.type.dinitype | Article | en_GB |
jgu.type.resource | Text | de |
jgu.type.version | Published version | de |
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