In 1968, John Thompson proved that a finite group G is solvable if and only
if every 2-generator subgroup of G is solvable. In this paper, we prove that
solvability of a finite group G is guaranteed by a seemingly weaker condition:
G is solvable if, for all conjugacy classes C and D of G consisting of elements
of prime power order, there exist x in C and y in D with x and y generating a
solvable group.