(untitled) (Communications in Mathematical Research, 2021)
The strong contact finite determinacy of relative map germs is studied by means of classical singularity theory. We first give the definition of a strong relative contact equivalence (or K_S,T equivalence) and then prove two theorems which can be used to distinguish the contact finite determinacy of relative map germs, that is, f is finite determined relative to K_S,T if and only if there exists a positive integer k, such that M^k (n)Ԑ(S; n)^p ⊂ TK_S,T(f).