UNICITY THEOREMS FOR MEROMORPHIC OR ENTIRE-FUNCTIONS .2.

In 1976, Gross posed the question ''can one find two (or possibly even one) finite sets S-j (j = 1, 2) such that any two entire functions f and g satisfying E(f)(S-j) = E(g)(S-j) for j = 1, 2 must be identical?'', where E(f)(S-j) stands for the inverse image of S-j under f. In this paper, we show that there exists a finite set S with 11 elements such that for any two non-constant meromorphic functions f and g the conditions E(f)(S) = E(g)(S) and E(f)({infinity}) = E(g)({infinity}) imply f equivalent to g. As a special case this also answers the question posed by Gross.