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ON CERTAIN APPLICATIONS OF THE KHUKHRO–MAKARENKO THEOREM

Published online by Cambridge University Press:  02 August 2012

AHMET ARIKAN
Affiliation:
Gazi Üniversitesi, Gazi Eǧitim Fakültesi, Matematik Eğitimi Anabilim Dalı 06500 Teknikokullar, Ankara, Turkey e-mail: arikan@gazi.edu.tr
HOWARD SMITH
Affiliation:
Department of Mathematics, Bucknell University, Lewisburg, PA 17837, USA e-mail: howsmith@bucknell.edu
NADIR TRABELSI
Affiliation:
Laboratory of Fundamental and Numerical Mathematics, Department of Mathematics, University Ferhat Abbas of Setif, Algeria e-mail: nadir_trabelsi@yahoo.fr
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Abstract

Some recent results of Khukhro and Makarenko on the existence of characteristic -subgroups of finite index in a group G, for certain varieties , are used to obtain generalisations of some well-known results in the literature pertaining to groups G, in which all proper subgroups satisfy some condition or other related to the property ‘soluble-by-finite’. In addition, a partial generalisation is obtained for the aforementioned results on the existence of characteristic subgroups.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

References

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ON CERTAIN APPLICATIONS OF THE KHUKHRO–MAKARENKO THEOREM
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