  Testing efficiently whether a finite set with a binary operation over it,
given as an oracle, is a group is a well-known open problem in the field of
property testing. Recently, Friedl, Ivanyos and Santha have made a significant
step in the direction of solving this problem by showing that it it possible to
test efficiently whether the input is an Abelian group or is far, with respect
to some distance, from any Abelian group. In this paper, we make a step further
and construct an efficient quantum algorithm that tests whether the input is a
solvable group, or is far from any solvable group. More precisely, the number
of queries used by our algorithm is polylogarithmic in the size of the set.
