Autoren:	Amberg, Bernhard Sysak, Yaroslav
Titel:	Products of locally cyclic groups
Online-Publikationsdatum:	4-Jul-2022
Erscheinungsdatum:	2021
Sprache des Dokuments:	Englisch
Zusammenfassung/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.
DDC-Sachgruppe:	510 Mathematik 510 Mathematics
Veröffentlichende Institution:	Johannes Gutenberg-Universität Mainz
Organisationseinheit:	FB 08 Physik, Mathematik u. Informatik
Veröffentlichungsort:	Mainz
ROR:	https://ror.org/023b0x485
DOI:	http://doi.org/10.25358/openscience-7289
Version:	Published version
Publikationstyp:	Zeitschriftenaufsatz
Nutzungsrechte:	CC BY
Informationen zu den Nutzungsrechten:	https://creativecommons.org/licenses/by/4.0/
Zeitschrift:	Archiv der Mathematik 117
Seitenzahl oder Artikelnummer:	19 28
Verlag:	Springer
Verlagsort:	Berlin u.a.
Erscheinungsdatum:	2021
ISSN:	1420-8938
DOI der Originalveröffentlichung:	10.1007/s00013-021-01593-1
Enthalten in den Sammlungen:	JGU-Publikationen