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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.


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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).



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