  The present paper deals with permutations induced by tame automorphisms over
finite fields. The first main result is a formula for determining the sign of
the permutation induced by a given elementary automorphism over a finite field.
The second main result is a formula for determining the sign of the permutation
induced by a given affine automorphism over a finite field. We also give a
combining method of the above two formulae to determine the sign of the
permutation induced by a given triangular automorphism over a finite field. As
a result, for a given tame automorphism over a finite field, if we know a
decomposition of the tame automorphism into a finite number of affine
automorphisms and elementary automorphisms, then one can easily determine the
sign of the permutation induced by the tame automorphism.
