TITLE:
Monotileable Amenable Groups: An Application
AUTHORS:
Amal Mohammed Ahmed Gaweash, Hayat Yousuf Ismail Bakur, Mariam Almahdi Mohammed Mulla
KEYWORDS:
Varieties of Groups, Abelian Groups, Multiplication, Amenable Groups, Lie Group, Følner Sequence
JOURNAL NAME:
Open Access Library Journal,
Vol.8 No.1,
January
29,
2021
ABSTRACT: We study actions of countable discrete groups which are Monotileable amenable groups in the sense that there exists a mean on X which is invariant under the action of G. Assuming that G is nonamenable, we obtain structural results for the stabilizer subgroups of amenable actions which allow us to relate the first l2-Betti number of G with that of the stabilizer subgroups.