Journal of Lie Theory

no. 1
On the Minimal Size of a Generating Set of Lattices in Lie Groups
Journal of Lie Theory, Volume 30 (2020) no. 1, pp. 33-40
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.
DOI: 10.5802/jolt.1103
Classification: 22E40
Keywords: Rank of lattices, lattices in Lie groups, finite generation, arithmetic groups 
@article{JOLT_2020_30_1_a3,
     author = {T. Gelander and R. Slutsky},
     title = {On the {Minimal} {Size} of a {Generating} {Set} of {Lattices} in {Lie} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {33--40},
     year = {2020},
     volume = {30},
     number = {1},
     doi = {10.5802/jolt.1103},
     zbl = {1440.22021},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1103/}
}
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T. Gelander; R. Slutsky. On the Minimal Size of a Generating Set of Lattices in Lie Groups. Journal of Lie Theory, Volume 30 (2020) no. 1, pp. 33-40. doi: 10.5802/jolt.1103

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