  We give a solution stated in the title to problem 3 of part 1 of the problems
listed in the book of Eklof and Mekler [EM],(p.453). There, in pp. 241-242,
this is discussed and proved in some cases. The existence of strongly
lambda-free ones was proved earlier by the criteria in [Sh:161] in [MkSh:251].
We can apply a similar proof to a large class of other varieties in particular
to the variety of (non-commutative) groups.
