Definition A subgroup of a group is termed strongly potentially characteristic if there is an embedding of the bigger group in some group such that, in that embedding both the group and the subgroup become characteristic.
One can refer this link: http://groupprops.wiki-site.com/index.php/Strongly_potentially_characteristic_subgroup
Although, i have somewhat understood the definition, i would like to have some examples of such subgroups. Moreover, i would also like to know, as to whats the essence of defining such subgroups in such a manner. Where are they applicable?