COHOPFIAN GROUPS AND ACCESSIBLE GROUP CLASSES

A group G is said to be cohopfian if it is neither trivial nor isomorphic to any of its proper subgroups, and this property is equivalent to the existence of a suitable group class (sic) such that G is minimal non-sic. If (sic) is any group class, the subclass (sic)degrees consisting of all groups that are isomorphic to proper subgroups of locally graded minimal non-(sic) groups is often much smaller than (sic). Similarly, if (sic)(prop) is the class of all groups isomorphic to proper subgroups of X-groups, the class <((sic))over bar> of all locally graded minimal non-(sic)(prop) groups may contain many groups which are not in (sic). This paper investigates the relation between the classes (sic), (sic)degrees and <((sic))over bar>.