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SEMIPERMUTABILITY IN GENERALISED SOLUBLE GROUPS

Part of: Representation theory of groups Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  02 November 2016

A. BALLESTER-BOLINCHES ,
J. C. BEIDLEMAN  and
R. IALENTI
A. BALLESTER-BOLINCHES*
Affiliation:
Departament de Matemàtiques, Universitat de València, Dr. Moliner, 50, 46100 Burjassot, València, Spain email [email protected]
J. C. BEIDLEMAN
Affiliation:
Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, USA email [email protected]
R. IALENTI
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Complesso Universitario Monte S. Angelo, Via Cintia, I-80126 Napoli, Italy email [email protected]
*
✉[email protected]
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Abstract

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Some classes of finitely generated hyperabelian groups defined in terms of semipermutability and S-semipermutability are studied in the paper. The classification of finitely generated hyperabelian groups all of whose finite quotients are PST-groups recently obtained by Robinson is behind our results. An alternative proof of such a classification is also included in the paper.

Keywords

generalised soluble groupspermutabilityS-semipermutability

MSC classification

Primary: 20E15: Chains and lattices of subgroups, subnormal subgroups
Secondary: 20D40: Products of subgroups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 95 , Issue 2 , April 2017 , pp. 219 - 227
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

Footnotes

The first author has been supported by the grant MTM2014-54707-C3-1-P from the Ministerio de Economía y Competitividad, Spain, and FEDER, European Union. He has also been supported by a project from the National Natural Science Foundation of China (NSFC, No. 11271085) and a project of the Natural Science Foundation of Guangdong Province (No. 2015A030313791).

References

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