  Let L be a simple finite-dimensional Lie algebra of characteristic distinct
from 2 and from 3. Suppose that L contains an extremal element that is not a
sandwich, that is, an element x such that [x, [x, L]] is equal to the linear
span of x in L. In this paper we prove that, with a single exception, L is
generated by extremal elements. The result is known, at least for most
characteristics, but the proofs in the literature are involved. The current
proof closes a gap in a geometric proof that every simple Lie algebra
containing no sandwiches (that is, ad-nilpotent elements of order 2) is in fact
of classical type.
