Geodesic
Decomposability of polymorphisms generated by an action of two finite groups
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XVIII, Tome 378 (2010), pp. 47-57

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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. 
@article{ZNSL_2010_378_a4,
     author = {A. M. Levin},
     title = {Decomposability of polymorphisms generated by an action of two finite groups},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {47--57},
     publisher = {mathdoc},
     volume = {378},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_378_a4/}
}
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A. M. Levin. Decomposability of polymorphisms generated by an action of two finite groups. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XVIII, Tome 378 (2010), pp. 47-57. http://geodesic.mathdoc.fr/item/ZNSL_2010_378_a4/