Abstract. Study of the normalizer of the MAD-group corresponding to a fine grading offers the most important tool for describing symmetries in the system of nonlinear equations connected with contraction of a Lie algebra. One fine grading that is always present in any Lie algebra sl(n,C) is the Pauli grading. The MAD-group corresponding to it is generated by generalized Pauli matrices. For such MAD-group, we already know its normalizer; its quotient group is isomorphic to the Lie group Sl(2, Z_n)×Z₂.
In this contribution, we deal with a more complicated situation, namely that the fine grading of sl(p²,C) is given by a tensor product of the Pauli matrices of the same order p, p being a prime. We describe the normalizer of the corresponding MAD-group and we show that its quotient group is isomorphic to Sp(2, Z_p)×Z₂.
This contribution is in fact a brief summary of the work by E. Pelantová, M. Svobodová, and S. Tremblay, which is in full contained in [1]. We refer the reader to that article for proofs of all the propositions and theorems stated in here.

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