Geodesic
On the Minimal Size of a Generating Set of Lattices in Lie Groups
Journal of Lie theory, Tome 30 (2020) no. 1, pp. 33-4
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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.
Classification : 22E40
Mots-clés : Rank of lattices, lattices in Lie groups, finite generation, arithmetic groups 
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     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--4},
     year = {2020},
     volume = {30},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JLT_2020_30_1_JLT_2020_30_1_a3/}
}
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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, Tome 30 (2020) no. 1, pp. 33-4. http://geodesic.mathdoc.fr/item/JLT_2020_30_1_JLT_2020_30_1_a3/