The scale function and lattices

Willis, G.

doi:10.1090/proc/13449

The scale function and lattices
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Proc. Amer. Math. Soc. 145 (2017), 3185-3190 Request permission

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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