Abstract
We introduce and study the concept of cyclicity degree of a finite group G. This quantity measures the probability of a random subgroup of G to be cyclic. Explicit formulas are obtained for some particular classes of finite groups. An asymptotic formula and minimality/maximality results on cyclicity degrees are also inferred.
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Tărnăuceanu, M., Tóth, L. Cyclicity degrees of finite groups. Acta Math. Hungar. 145, 489–504 (2015). https://doi.org/10.1007/s10474-015-0480-2
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DOI: https://doi.org/10.1007/s10474-015-0480-2