We discuss some methods for determining transversals under group actions on sets of functions. Especially the following problems will be investigated:
The homomorphism principle can be used for determining a complete set of orbit representatives for group actions on the range of functions. This method can be combined with the well known techniques for group actions on the domain of functions, so that orbit representatives for actions both on the domain and on the range can be computed.
Lehmann's Lemma demonstrates, how the exponentiation of two permutation groups can be replaced by two simpler group actions. This method can be applied both for computation of transversals and for generation of orbit representatives uniformly at random under the group action of the exponentiation.