  This is an old paper put here for archeological purposes. It is proved that a
finite-dimensional Lie algebra over a field of characteristic p>5, that can be
written as a vector space (not necessarily direct) sum of two nilpotent
subalgebras, is solvable. The same result (but covering also the cases of low
characteristics) was established independently by V. Panyukov (Russ. Math.
Surv. 45 (1990), N4, 181-182), and the homological methods utilized in the
proof were developed later in arXiv:math/0204004. Many inaccuracies in the
English translation are corrected, otherwise the text is identical to the
published version.
