On the Prüfer rank of mutually permutable products of abelian groups

A. Ballester-Bolinches; John Cossey; H. Meng; M. C. Pedraza-Aguilera

doi:10.1007/s10231-018-0800-6

On the Prüfer rank of mutually permutable products of abelian groups

A. Ballester-Bolinches^*, John Cossey, H. Meng, M. C. Pedraza-Aguilera

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

A group G has finite (or Prüfer or special) rank if every finitely generated subgroup of G can be generated by r elements and r is the least integer with this property. The aim of this paper is to prove the following result: assume that G= AB is a group which is the mutually permutable product of the abelian subgroups A and B of Prüfer ranks r and s, respectively. If G is locally finite, then the Prüfer rank of G is at most r+ s+ 3. If G is an arbitrary group, then the Prüfer rank of G is at most r+ s+ 4.

Original language	English
Pages (from-to)	811-819
Number of pages	9
Journal	Annali di Matematica Pura ed Applicata
Volume	198
Issue number	3
DOIs	https://doi.org/10.1007/s10231-018-0800-6
Publication status	Published - 1 Jun 2019

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title = "On the Pr{\"u}fer rank of mutually permutable products of abelian groups",

abstract = "A group G has finite (or Pr{\"u}fer or special) rank if every finitely generated subgroup of G can be generated by r elements and r is the least integer with this property. The aim of this paper is to prove the following result: assume that G= AB is a group which is the mutually permutable product of the abelian subgroups A and B of Pr{\"u}fer ranks r and s, respectively. If G is locally finite, then the Pr{\"u}fer rank of G is at most r+ s+ 3. If G is an arbitrary group, then the Pr{\"u}fer rank of G is at most r+ s+ 4.",

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author = "A. Ballester-Bolinches and John Cossey and H. Meng and Pedraza-Aguilera, {M. C.}",

note = "Publisher Copyright: {\textcopyright} 2018, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature.",

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doi = "10.1007/s10231-018-0800-6",

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T1 - On the Prüfer rank of mutually permutable products of abelian groups

AU - Ballester-Bolinches, A.

AU - Cossey, John

AU - Meng, H.

AU - Pedraza-Aguilera, M. C.

PY - 2019/6/1

Y1 - 2019/6/1

N2 - A group G has finite (or Prüfer or special) rank if every finitely generated subgroup of G can be generated by r elements and r is the least integer with this property. The aim of this paper is to prove the following result: assume that G= AB is a group which is the mutually permutable product of the abelian subgroups A and B of Prüfer ranks r and s, respectively. If G is locally finite, then the Prüfer rank of G is at most r+ s+ 3. If G is an arbitrary group, then the Prüfer rank of G is at most r+ s+ 4.

AB - A group G has finite (or Prüfer or special) rank if every finitely generated subgroup of G can be generated by r elements and r is the least integer with this property. The aim of this paper is to prove the following result: assume that G= AB is a group which is the mutually permutable product of the abelian subgroups A and B of Prüfer ranks r and s, respectively. If G is locally finite, then the Prüfer rank of G is at most r+ s+ 3. If G is an arbitrary group, then the Prüfer rank of G is at most r+ s+ 4.

KW - Abelian group

KW - Factorisations

KW - Polycyclic group

KW - Rank

KW - Soluble group

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M3 - Article

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JO - Annali di Matematica Pura ed Applicata

JF - Annali di Matematica Pura ed Applicata

IS - 3

ER -

On the Prüfer rank of mutually permutable products of abelian groups

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