Products of locally cyclic groups

dc.contributor.authorAmberg, Bernhard
dc.contributor.authorSysak, Yaroslav
dc.date.accessioned2022-07-04T08:32:42Z
dc.date.available2022-07-04T08:32:42Z
dc.date.issued2021
dc.description.abstractWe 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.doihttp://doi.org/10.25358/openscience-7289
dc.identifier.urihttps://openscience.ub.uni-mainz.de/handle/20.500.12030/7303
dc.language.isoengde
dc.rightsCC-BY-4.0*
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/*
dc.subject.ddc510 Mathematikde_DE
dc.subject.ddc510 Mathematicsen_GB
dc.titleProducts of locally cyclic groupsen_GB
dc.typeZeitschriftenaufsatzde
jgu.journal.titleArchiv der Mathematikde
jgu.journal.volume117de
jgu.organisation.departmentFB 08 Physik, Mathematik u. Informatikde
jgu.organisation.nameJohannes Gutenberg-Universität Mainz
jgu.organisation.number7940
jgu.organisation.placeMainz
jgu.organisation.rorhttps://ror.org/023b0x485
jgu.pages.end28de
jgu.pages.start19de
jgu.publisher.doi10.1007/s00013-021-01593-1de
jgu.publisher.issn1420-8938de
jgu.publisher.nameSpringerde
jgu.publisher.placeBerlin u.a.de
jgu.publisher.year2021
jgu.rights.accessrightsopenAccess
jgu.subject.ddccode510de
jgu.type.dinitypeArticleen_GB
jgu.type.resourceTextde
jgu.type.versionPublished versionde

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