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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 $\mathcal{K}_{S,T}$ 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 $\mathcal{K}_{S,T}$ if and only if there exists a positive integer $k$, such that $\mathcal{M}^k (n)Ԑ(S; n)^p ⊂ T\mathcal{K}_{S,T}(f)$.
}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19172.html} }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 $\mathcal{K}_{S,T}$ 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 $\mathcal{K}_{S,T}$ if and only if there exists a positive integer $k$, such that $\mathcal{M}^k (n)Ԑ(S; n)^p ⊂ T\mathcal{K}_{S,T}(f)$.