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Abstract
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A –structure on a
group , defined by
M Bestvina, is a pair
of spaces such that
is a compact ER,
is a –set
in ,
acts properly and
cocompactly on
and the collection of translates of any compact set in
forms a null
sequence in .
It is natural to ask whether a given group admits a
–structure.
In this paper, we show that if two groups each admit a
–structure,
then so do their free and direct products.
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Keywords
$\mathcal{Z}$–structure, boundary, free product, direct
product, product group
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Mathematical Subject Classification 2010
Primary: 57M07
Secondary: 20F65
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Publication
Received: 14 October 2010
Accepted: 24 June 2011
Published: 16 September 2011
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