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We determine the minimal number of separating invariants for the invariant ring of a matrix group G ≤ GL n (F q) over the finite field F q. We show that this minimal number can be obtained with invariants of degree at most | G | n (q − 1). In the non-modular case this construction can be improved to give invariants of degree at most n (q − 1). As examples we study separating invariants over the field F 2 for two important representations of the symmetric group. [ABSTRACT FROM AUTHOR]