The it is easy to prove:  The motivation for the definition of wrappable class comes from results such as the Boone-Higman theorem, which states that a countable group "G" has soluble word problem if and only if it can be embedded in a simple group "S" that can be embedded in a finitely presented group "F". Houcine has shown that the group "F" can be constructed so that it too has soluble word problem. This together with the fact that taking the direct product of two groups preserves solubility of the word problem shows that:  Other examples of wrappable classes of groups are:  The fact that a class formula_9 is wrappable does not imply that any groups are SQ-universal for formula_9. It is clear, for instance, that some sort of cardinality restriction for the members of formula_9 is required. If we replace the phrase "isomorphic to a subgroup of a quotient of" with "isomorphic to a subgroup of" in the definition of "SQ-universal", we obtain the stronger concept of S-universal (respectively S-universal for/in formula_9). The Higman Embedding Theorem can be used to prove that there is a finitely presented group that contains a copy of every finitely presented group. If formula_36 is the class of all finitely presented groups with soluble word problem, then it is known that there is no uniform algorithm to solve the word problem for groups in formula_36. It follows, although the proof is not a straightforward as one might expect, that no group in formula_36 can contain a copy of every group in formula_36. But it is clear that any SQ-universal group is "a fortiori" SQ-universal for formula_36. If we let formula_41 be the class of finitely presented groups, and "F"2 be the free group on two generators, we can sum this up as:  The following questions are open (the second implies the first):  While it is quite difficult to prove that "F"2 is SQ-universal, the fact that it is SQ-universal "for the class of finite groups" follows easily from these two facts:  If formula_48 is a category and formula_9 is a class of objects of formula_48, then the definition of "SQ-universal for formula_9" clearly makes sense. If formula_48 is a concrete category, then the definition of "SQ-universal in formula_9" also makes sense.