This work demonstrates a bound on generating set size in lattices of connected Lie groups, extending previous theorems.
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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Gelander et al. (2020) studied this question.
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