Authors:	Amberg, Bernhard Sysak, Yaroslav
Title:	Products of locally cyclic groups
Online publication date:	4-Jul-2022
Year of first publication:	2021
Language:	english
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:	510 Mathematik 510 Mathematics
Institution:	Johannes Gutenberg-Universität Mainz
Department:	FB 08 Physik, Mathematik u. Informatik
Place:	Mainz
ROR:	https://ror.org/023b0x485
DOI:	http://doi.org/10.25358/openscience-7289
Version:	Published version
Publication type:	Zeitschriftenaufsatz
License:	CC BY
Information on rights of use:	https://creativecommons.org/licenses/by/4.0/
Journal:	Archiv der Mathematik 117
Pages or article number:	19 28
Publisher:	Springer
Publisher place:	Berlin u.a.
Issue date:	2021
ISSN:	1420-8938
Publisher DOI:	10.1007/s00013-021-01593-1
Appears in collections:	JGU-Publikationen