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
SN - 0002-9947
VL - 305
SP - 369
EP - 376
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 1
ER -