  The concept of configuration was first introduced by Rosenblatt and Willis to
give a characterization for the amenability of groups. We show that group
properties of being soluble or FC can be characterized by configuration sets.
Then we investigate some condition on configuration pairs, which leads to
isomorphism. We introduce a somewhat different notion of configuration
equivalence, namely strong configuration equivalence, and prove that strong
configuration equivalence coincides with isomorphism.
