Transformation groups in quaternions space

In this study, in quaternions space the results for quaternions have been found. SU(2) ? equivalence problem of points system in C^2- space and K_1- equivalence problem of points system in quaternions space were defined. From quaternion space to vector space a transformation was defined. This transformation was shown to be a C - isomorphism. Also this transformation was shown to be a group isomorphism. Using this result, correlations between SU(2) ? equivalence problem and K_1- equivalence problem has been studied. Further, K_1- equivalence problem has been solved. SU(2) ? equivalence problem has been solved in C^2- space by using this connection with the help of quaternions.Key Words: : Quaternion, Invariant, Equivalence Problem.