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: