Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-24T03:54:47.935Z Has data issue: false hasContentIssue false
  • English
  • Français

SOME SOLUBILITY CRITERIA IN FACTORISED GROUPS

Part of: Representation theory of groups

Published online by Cambridge University Press:  02 February 2012

M. ASAAD ,
A. BALLESTER-BOLINCHES  and
R. ESTEBAN-ROMERO
M. ASAAD
Affiliation:
Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt (email: [email protected])
A. BALLESTER-BOLINCHES*
Affiliation:
Departament d’Àlgebra, Universitat de València, Dr. Moliner 50, 46100 Burjassot, València, Spain (email: [email protected])
R. ESTEBAN-ROMERO
Affiliation:
Institut Universitari de Matemàtica Pura i Aplicada, Universitat Politècnica de València, Camí de Vera s/n, 46022 València, Spain (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, solubility of groups factorised as a product of two subgroups which are connected by certain permutability properties is studied.

Keywords

factorised groupmutually m-permutable productsoluble group

MSC classification

Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 86 , Issue 1 , August 2012 , pp. 22 - 28
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

Footnotes

The research of the second and the third authors has been supported by the grant MTM2010-19938-C03-01 from the Ministerio de Ciencia e Innovación (Spanish government).

References

[1]Amberg, B., Franciosi, S. and de Giovanni, F., Products of Groups, Oxford Mathematical Monographs (Clarendon Press, New York, 1992).Google Scholar
[2]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
[3]Ballester-Bolinches, A., Esteban-Romero, R. and Asaad, M., Products of Finite Groups, de Gruyter Expositions in Mathematics, 53 (Walter de Gruyter, Berlin, 2010).CrossRefGoogle Scholar
[4]Ballester-Bolinches, A., Guo, X. and Pedraza-Aguilera, M. C., ‘A note on m-permutable products of finite groups’, J. Group Theory 3(4) (2000), 381–384.CrossRefGoogle Scholar
[5]Deskins, W. E., ‘On maximal subgroups’, Proc. Sympos. Pure Math. Amer. Math. Soc. 1 (1959), 100–104.CrossRefGoogle Scholar
[6]Doerk, K. and Hawkes, T., Finite Soluble Groups, De Gruyter Expositions in Mathematics, 4 (Walter de Gruyter, Berlin–New York, 1992).CrossRefGoogle Scholar
[7]Ezquerro, L. M. and Soler-Escrivà, X., ‘On mutually M-permutable products of finite groups’, Comm. Algebra 31(4) (2003), 1949–1960.CrossRefGoogle Scholar
[8]Huppert, B., Endliche Gruppen I, Grundlehren Math. Wiss., 134 (Springer, Berlin–Heidelberg–New York, 1967).CrossRefGoogle Scholar
[9]Maier, R., ‘Zur Vertauschbarkeit und Subnormalität von Untergruppen’, Arch. Math. (Basel) 53 (1989), 110–120.CrossRefGoogle Scholar