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

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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 card(G///) < caid(H).

Original languageEnglish (US)
Pages (from-to)369-376
Number of pages8
JournalTransactions of the American Mathematical Society
Volume305
Issue number1
DOIs
StatePublished - Jan 1988
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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