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

Krasa, Stefan

doi:10.1090/S0002-9947-1988-0920164-X

The action of a solvable group on an infinite set never has a unique invariant mean
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by Stefan Krasa PDF

Trans. Amer. Math. Soc. 305 (1988), 369-376 Request permission

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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