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F{\o}lner Nets for Semidirect Products of Amenable Groups

  Published:2008-03-01
 Printed: Mar 2008
  • David Janzen
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Abstract

For unimodular semidirect products of locally compact amenable groups $N$ and $H$, we show that one can always construct a F{\o}lner net of the form $(A_\alpha \times B_\beta)$ for $G$, where $(A_\alpha)$ is a strong form of F{\o}lner net for $N$ and $(B_\beta)$ is any F{\o}lner net for $H$. Applications to the Heisenberg and Euclidean motion groups are provided.
MSC Classifications: 22D05, 43A07, 22D15, 43A20 show english descriptions General properties and structure of locally compact groups
Means on groups, semigroups, etc.; amenable groups
Group algebras of locally compact groups
$L^1$-algebras on groups, semigroups, etc.
22D05 - General properties and structure of locally compact groups
43A07 - Means on groups, semigroups, etc.; amenable groups
22D15 - Group algebras of locally compact groups
43A20 - $L^1$-algebras on groups, semigroups, etc.
 

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