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arXiv · 1903.04828

On the Minimal Size of a Generating Set of Lattices in Lie Groups

Tsachik Gelander·Raz Slutsky
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Abstract

We prove that the rank (that is, the minimal size of a generating set) of lattices in a general connected Lie group is bounded by the co-volume of the projection of the lattice to the semi-simple part of the group. This was proved by Gelander for semi-simple Lie groups and by Mostow for solvable Lie groups. Here we consider the general case, relying on the semi-simple case. In particular, we extend Mostow's theorem from solvable to amenable groups.

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Tsachik Gelander, Raz Slutsky. 2019-03-12. On the Minimal Size of a Generating Set of Lattices in Lie Groups. https://arxiv.org/abs/1903.04828

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