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The scale function and lattices


Author: G. A. Willis
Journal: Proc. Amer. Math. Soc. 145 (2017), 3185-3190
MSC (2010): Primary 22D05; Secondary 20E34, 22E40
DOI: https://doi.org/10.1090/proc/13449
Published electronically: January 23, 2017
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Abstract: It is shown that, given a lattice $ H$ in a totally disconnected, locally compact group $ G$, the contraction subgroups in $ G$ and the values of the scale function on $ G$ are determined by their restrictions to $ H$. Group theoretic properties intrinsic to the lattice, such as being periodic or infinitely divisible, are then seen to imply corresponding properties of $ G$.


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Additional Information

G. A. Willis
Affiliation: School of Mathematical and Physical Sciences, The University of Newcastle, University Drive, Building V, Callaghan, NSW 2308, Australia
Email: George.Willis@newcastle.edu.au

DOI: https://doi.org/10.1090/proc/13449
Keywords: Scale function, finite co-volume, lattice, uniscalar, anisotropic
Received by editor(s): July 7, 2015
Received by editor(s) in revised form: August 27, 2016
Published electronically: January 23, 2017
Additional Notes: The author was supported by ARC Discovery Project DP150100060
Communicated by: Kevin Whyte
Article copyright: © Copyright 2017 American Mathematical Society