Abstract
Let {mathfrak {X}} be a group class. A group G is an opponent of {mathfrak {X}} if it is not an {mathfrak {X}}-group, but all its proper subgroups belong to {mathfrak {X}}. Of course, every opponent of {mathfrak {X}} is a cohopfian group and the aim of this paper is to describe the smallest group class containing {mathfrak {X}} and admitting no such a kind of cohopfian groups.
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