On Certain Applications of the Khukhro-Makarenko Theorem
Glasgow Mathematical Journal
Some recent results of Khukhro and Makarenko on the existence of characteristic X-subgroups of finite index in a group G, for certain varieties X, 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.
Arikan, Ahmet; Smith, Howard; and Trabelsi, Nadir. "On Certain Applications of the Khukhro-Makarenko Theorem." Glasgow Mathematical Journal 55, no. 2 (2013) : 275-283.