Decomposability of polymorphisms generated by an action of two finite groups

In this paper, we consider problems related to the decomposability of multivalued measure-preserving transformations (i.e., polymorphisms) generated by an action of two finite groups on a Lebesgue space. We give a general construction of such polymorphisms and prove a convenient decomposability criterion. In the case where both generating groups are of order 2, we use this criterion to further characterize the decomposability. In the last section, we present a method of constructing an approximative decomposition of polymorphisms that can be used for obtaining a decomposition in the usual sense. Bibl. 6 titles.