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 
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/
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     title = {Decomposability of polymorphisms generated by an action of two finite groups},
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     year = {2010},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_378_a4/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.

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[3] A. M. Vershik, “Kak vyglyadit tipichnyi markovskii operator?”, Algebra i analiz, 17:5 (2005), 91–104 | MR | Zbl

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[5] A. G. Kurosh, Teoriya grupp, Nauka, M., 1967 | MR | Zbl

[6] V. A. Rokhlin, “Ob osnovnykh ponyatiyakh teorii mery”, Mat. sb., 25(67):1 (1949), 107–150 | MR | Zbl