Abstract
Let G be a finite group and let A be a finite sequence of subsets of G. We consider covers for the group G of the type A k, where A k is the concatenation of k copies of A. We show that the distribution of the elements of G generated by A k approaches the uniform distribution as k → ∞ (in the ℓ ∞-norm). If G = PSL(2, p) and \({{\bf A}=( \langle \alpha \rangle, \langle \beta \rangle )}\) , where α and β are two non-commuting generators of order p, we provide the exact distribution of the elements generated by A k.
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Pace, N. On the distribution of the elements of a finite group generated by covers. AAECC 22, 367–373 (2011). https://doi.org/10.1007/s00200-011-0156-2
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DOI: https://doi.org/10.1007/s00200-011-0156-2