 This means that for any
residue class formula_6 there are coefficients
formula_7
such that the restriction of the mapping formula_4
to the set formula_9 is given by

Residue-class-wise affine groups are countable, and they are accessible
to computational investigations.Many of them act multiply transitively on formula_1 or on subsets thereof.A particularly basic type of residue-class-wise affine permutations are the
class transpositions