  Universality has been an important concept in computable structure theory. A
class $\mathcal{C}$ of structures is universal if, informally, for any
structure, of any kind, there is a structure in $\mathcal{C}$ with the same
computability-theoretic properties as the given structure. Many classes such as
graphs, groups, and fields are known to be universal.
  This paper is about the class of finitely generated groups. Because finitely
generated structures are relatively simple, the class of finitely generated
groups has no hope of being universal. We show that finitely generated groups
are as universal as possible, given that they are finitely generated: for every
finitely generated structure, there is a finitely generated group which has the
same computability-theoretic properties. The same is not true for finitely
generated fields. We apply the results of this investigation to quasi Scott
sentences.
