Residual finiteness of quasi-positive one-relator groups

A criterion is given for showing that certain one-relator groups are residually finite. This is applied to a one-relator group with torsion G = <a(1),...,a(r), \ W-n>. It is shown that G is residually finite provided that W is outside the commutator subgroup and n is sufficiently large. An important ingredient in the proof is a criterion which implies that a: subgroup of a group is malnormal. A graded small-cancellation criterion is developed which detects whether a map A --> B between graphs induces a pi-injection, and whether pi(1)A maps to a malnormal subgroup of pi(1)B.