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Zap. Nauchn. Sem. POMI, 2010, Volume 378, Pages 47–57 (Mi znsl3827)  

Decomposability of polymorphisms generated by an action of two finite groups

A. M. Levin

Saint-Petersburg State University, Saint-Petersburg, Russia

Abstract: 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.

Key words and phrases: polymorphism, decomposability.

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English version:
Journal of Mathematical Sciences (New York), 2011, 174:1, 23–27

UDC: 517.987.5
Received: 29.09.2010

Citation: A. M. Levin, “Decomposability of polymorphisms generated by an action of two finite groups”, Representation theory, dynamical systems, combinatorial methods. Part XVIII, Zap. Nauchn. Sem. POMI, 378, POMI, St. Petersburg, 2010, 47–57; J. Math. Sci. (N. Y.), 174:1 (2011), 23–27

Citation in format AMSBIB
\Bibitem{Lev10}
\by A.~M.~Levin
\paper Decomposability of polymorphisms generated by an action of two finite groups
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XVIII
\serial Zap. Nauchn. Sem. POMI
\yr 2010
\vol 378
\pages 47--57
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3827}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2011
\vol 174
\issue 1
\pages 23--27
\crossref{https://doi.org/10.1007/s10958-011-0277-y}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79952815144}


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