  Let X be a K3 surface with the Neron-Severi lattice S_X and transcendental
lattice T_X. Nukulin considered the kernel H_X of the natural representation
Aut(X) ---> O(S_X) and proved that H_{X} is a finite cyclic group with
phi(h(X))) | t(X) and acts faithfully on the space H^{2,0}(X) = C omega_{X},
where h(X) = ord(H_X), t(X) = rank T_X and phi(.) is the Euler function.
Consider the extremal case where phi(h(X)) = t(X). In the situation where T_{X}
is unimodular, Kondo has determined the list of t(X), as well as the actual
realizations, and showed that t(X) alone uniquely determines the isomorphism
class of X (with phi(h(X)) = t(X)). We settle the remaining situation where T_X
is not unimodular. Together, we provide the proof for the theorem announced by
Vorontsov.
