  The Kruglov property and the Kruglov operator play an important role in the
study of geometric properties of r.i. function spaces. We prove that the
boundedness of the Kruglov operator in a r.i. space is equivalent to the
uniform boundedness on this space of a sequence of operators defined by random
permutations. It is shown also that there is no minimal r.i. space with the
Kruglov property.
