Title: Polynomial structures on polycyclic groups
Authors: Dekimpe, Karel * ×
Igodt, Paul G. * #
Issue Date: Sep-1997
Publisher: Amer mathematical soc
Series Title: Transactions of the american mathematical society vol:349 issue:9 pages:3597-3610
Abstract: We know, by recent work of Benoist and of Burde & Grunewald, that there exist polycyclic-by-finite groups G, of rank h (the examples given were in fact nilpotent), admitting no properly discontinuous affine action on R-h. On the other hand, for such G, it is always possible to construct a properly discontinuous smooth action of G on R-h. Our main result is that any polycyclic-by-finite group G of rank h contains a subgroup of finite index acting properly discontinuously and by polynomial diffeomorphisms of bounded degree on R-h. Moreover, these polynomial representations always appear to contain pure translations and are extendable to a smooth action of the whole group G.
ISSN: 0002-9947
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Mathematics, Campus Kulak Kortrijk
* (joint) first author
× corresponding author
# (joint) last author

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