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We investigate the exact relations between the renormalization group functions for certain supersymmetric theories and the dependence of these relations on a renormalization prescription. In particular, it is demonstrated that sometimes the running of various couplings can be related in all orders. The corresponding equations can be written in the form of some renormalization group invariant expressions. Two such expressions are constructed for MSSM. For some models the general statements about the running of couplings are verified by explicit calculations done in the approximations where the scheme dependence becomes essential.
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