In connected compact Lie groups the maximal size of an irredundant topologically generating set is bounded by a polynomial in the rank, with analogous statements for amenable Lie groups and reductive algebraic groups.
On the maximal size of independent generating sets of PSL2 (q)
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On the Maximal Size of Irredundant Generating Sets in Lie Groups and Algebraic Groups
In connected compact Lie groups the maximal size of an irredundant topologically generating set is bounded by a polynomial in the rank, with analogous statements for amenable Lie groups and reductive algebraic groups.