  Let Z be an affine algebraic variety and ED(Z)= max(2 dim Z+1, dim TZ). Let X
be a smooth algebraic variety isomorphic to a semi-simple linear algebraic
group whose Lie algebra is a sum of special linear Lie algebras. We show that
if dim X > ED(Z) -1, then Z admits a closed embedding into X. We also show that
for every smooth affine flexible variety Y there is a closed embedding of $Z$
into the the product of Y and an affine n-space provided that n > dim Z- 2 and
dim Y +n > ED (Z) -1.
