Cyclicity degrees of finite groups
  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 several minimality/maximality results on cyclicity degrees are also inferred. 
Marius T\u{a}rn\u{a}uceanu, L\'aszl\'o T\'oth
math.GR