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ON CERTAIN APPLICATIONS OF THE KHUKHRO–MAKARENKO THEOREM
AHMET ARIKAN, HOWARD SMITH, NADIR TRABELSI
Journal:

Glasgow Mathematical Journal / Volume 55 / Issue 2 / May 2013

Published online by Cambridge University Press:

02 August 2012, pp. 275-283

Print publication:

May 2013
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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.