TY - JOUR

T1 - The action of a solvable group on an infinite set never has a unique invariant mean

AU - Krasa, Stefan

N1 - Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

PY - 1988/1

Y1 - 1988/1

N2 - 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).

AB - 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).

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U2 - 10.1090/S0002-9947-1988-0920164-X

DO - 10.1090/S0002-9947-1988-0920164-X

M3 - Article

AN - SCOPUS:84966227579

VL - 305

SP - 369

EP - 376

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 1

ER -