Abstract
Suppose G is a finite abelian group with minimal number of generators r. It is shown that the expected number of elements from G (chosen independently and with the uniform distribution) so that the elements chosen generate G is less than r + where= 2118456563...The constant is explicitly described in terms of the Riemann zeta-function and is best possible.
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Pomerance, C. The expected number of random elements to generate a finite abelian group. Periodica Mathematica Hungarica 43, 191–198 (2002). https://doi.org/10.1023/A:1015250102792
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DOI: https://doi.org/10.1023/A:1015250102792