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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The action of a solvable group on an infinite set never has a unique invariant mean


Author: Stefan Krasa
Journal: Trans. Amer. Math. Soc. 305 (1988), 369-376
MSC: Primary 43A07
DOI: https://doi.org/10.1090/S0002-9947-1988-0920164-X
MathSciNet review: 920164
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Abstract: Theorem 1 of the paper proves a conjecture of J. Rosenblatt on nonuniqueness of invariant means for the action of a solvable group $ G$ on an infinite set $ X$. The same methods used in this proof yield even a more general result: Nonuniqueness still holds if $ G$ is an amenable group containing a solvable subgroup $ H$ such that $ \operatorname{card} (G/H) \leqslant \operatorname{card} (H)$.


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DOI: https://doi.org/10.1090/S0002-9947-1988-0920164-X
Article copyright: © Copyright 1988 American Mathematical Society