  It is known that connected sums of positive torus knots are not concordant to
$L$-space knots. Here we consider differences of torus knots. The main result
states that the subgroup of the concordance group generated by two positive
torus knots contains no nontrivial $L$-space knots other than the torus knots
themselves. Generalizations to subgroups generated by more than two torus knots
are also considered.
