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ON A THEOREM OF KANG AND LIU ON FACTORISED GROUPS

Part of: Representation theory of groups

Published online by Cambridge University Press:  08 November 2017

A. BALLESTER-BOLINCHES  and
M. C. PEDRAZA-AGUILERA
A. BALLESTER-BOLINCHES*
Affiliation:
Departament de Matemàtiques, Universitat de València, Dr. Moliner 50, 46100 Burjassot, València, Spain email Adolfo.Ballester@uv.es
M. C. PEDRAZA-AGUILERA
Affiliation:
Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera, 46022, Valencia, Spain email mpedraza@mat.upv.es
*
✉ Adolfo.Ballester@uv.es
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Abstract

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Kang and Liu [‘On supersolvability of factorized finite groups’, Bull. Math. Sci.3 (2013), 205–210] investigate the structure of finite groups that are products of two supersoluble groups. The goal of this note is to give a correct proof of their main theorem.

Keywords

finite groupfactorisationssupersolubility

MSC classification

Primary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks
Secondary: 20D20: Sylow subgroups, Sylow properties, $pi$-groups, $pi$-structure 20D40: Products of subgroups

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 97 , Issue 1 , February 2018 , pp. 54 - 56
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

Footnotes

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

References

Amberg, B., Franciosi, S. and De Giovanni, F., Products of Groups, Oxford Mathematical Monographs (Clarendon Press, Oxford, 1992).Google Scholar
Ballester-Bolinches, A., Cossey, J. and Pedraza-Aguilera, M. C., ‘On products of finite supersoluble groups’, Comm. Algebra 29(7) (2001), 3145–3152.CrossRefGoogle Scholar
Ballester-Bolinches, A., Esteban-Romero, R. and Asaad, M., Products of Finite Groups, Gruyter Expositions in Mathematics, 53 (Walter de Gruyter, Berlin, 2010).Google Scholar
Ezquerro, L. M. and Soler-Escrivà, X., ‘On mutually m-permutable products of finite groups’, Comm. Algebra 31(4) (2003), 1949–1960.Google Scholar
Kang, P. and Liu, Q., ‘On supersolvability of factorized finite groups’, Bull. Math. Sci. 3 (2013), 205–210.Google Scholar