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